Clusteranalyse
Peter Zezula
Clustering Prinzipien
Agglomerative Hierarchical Clustering
Alle Personen werden nach einem Distanzmaß successive zu Clustern zusammengefasst, bis alle Personen in einem einzigen Cluster sind. Auf einem bestimmten Niveau kann man die Zuordnung der Personen zu den Clustern interpretieren. Hierbei spielen die Unterschiede im Distanzmaß zwischen den Clustern eine Rolle. Eine Visualisierung mithilfe eines Dentrogramms hilft hierbei.
k-Means Clustering
Die Beobachtungen sollen einer fest vorgegebenen Anzahl von Clustern zugeordnet werden. Kriterium der besten Lösung kann z. B. das Minimieren der Binnenvarianz der resultierenden Cluster sein (within group sum of squares). Problem: Die Lösung ist abhängig von der Skalierung der Variablen (s.u. ) Problem: Systematisches Permutieren aller Personen-Cluster-Kombinationen wächst exponentiell.
Model-Based Clustering.
Über Maximum Likelihood Schätzungen wird ein möglichst gut an die Daten angepasstes Modell ermittelt.
Euclidean Distance
\[ d_{ij} = \sqrt{\sum_{k=1}^{q}{(x_{ik} - x_{jk})^2}} \] i, j: individuals \ variables: \(x_{j1}, x_{j2}, ..., x_{jq}\)
dist()
dist() erzeugt eine Distanzmatrix.
Default Euklidische Distanz. Quadrierte Differenz zwischen je zwei Vpn in einer Variable, über die Variablen summiert und daraus die Wurzel ist die euklidische Distanz zwischen diesen beiden Vpn.
Da verschiedene Variablen, nach denen geclustert wird, je nach
Skalierung unterschiedlich hoch in das Distanzmaß eingehen, kann es
sinnvoll sein, die Maße vorher zu normieren (z-transformieren).
scale() dient hierzu.
hclust()
hclust() clustert hclust(dmat, method = “complete”)
methods:
- single: the smallest distance between the objects being clustered
- complete: the largest distance between the objects being clustered
- average: the average distance between the objects being clustered
Dendrogramm mit plot()
Ein Dendrogramm erstellt man, indem man plot() auf ein hclust()-Objekt aufruft.
Zugehörigkeit zu Clustern: cutree()
cutree() wird auf ein hclust()-Objekt angewendet und erzeugt einen Vektor mit der Zugehörigkeit der Beobachtungen zu den Clustern.
Parameter h: ‘Schneidet’ das Dendrogramm auf dieser Höhe auf. Parameter k: Teilt die Stichprobe in k Gruppen/Cluster auf, wählt also die zugehörige Höhe.
plot(hclust())
Plottet eine Clusteranalyse vom Typ hclust.
kmeans()
Vorgegebene Anzahl von Clustern: kmeans()
Bei vorgegebener Anzahl von Clustern werden die Beobachtungen so aufgeteilt, dass die Distanzen innerhalb der Gruppen minimiert werden.
kmeans(x, n) x ist Datenmatrix n ist Anzahl der Cluster
Beispiele aus Everitt (2010)
Beispiel: Body Data (Everitt, 2010)
Körpermaße: Brust, Bauch, Hüfte von 20 Vpn.
d.body <- read.delim(file="http://md.psych.bio.uni-goettingen.de/mv/data/div/mv_body.txt")
# zeige DataFrame
head(d.body)## Chest Waist Hips
## 1 34 30 32
## 2 37 32 37
## 3 38 30 36
## 4 36 33 39
## 5 38 29 33
## 6 43 32 38attach(d.body)
#
options(digits=3)
# eine Matrix der euklidischen Distanzen erzeugen
distances<-dist(d.body)
# Agglomerativer Algorithmus
h.body <- hclust(distances,method="single")
print(hclust(distances,method="single"))##
## Call:
## hclust(d = distances, method = "single")
##
## Cluster method : single
## Distance : euclidean
## Number of objects: 20# was gibt es alles im Ergebnisobjekt?
str(hclust(distances,method="single"))## List of 7
## $ merge : int [1:19, 1:2] -12 -15 -16 -11 -13 -8 -3 -6 3 5 ...
## $ height : num [1:19] 1 1 1 1.41 1.41 ...
## $ order : int [1:20] 1 7 5 6 10 4 2 3 9 8 ...
## $ labels : NULL
## $ method : chr "single"
## $ call : language hclust(d = distances, method = "single")
## $ dist.method: chr "euclidean"
## - attr(*, "class")= chr "hclust"# Dendrogramm
plot(hclust(distances,method="single"))
# Zuordnung der Vpn zu Clustern, entweder in Abhängigkeit von der Höhe
# oder mit Vorgabe der Menge der Cluster
body_sl3<-cutree(hclust(distances,method="single"),h=3.8)
body_sl3## [1] 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2# alternativ mit Angabe der Cluster
body_sl3<-cutree(hclust(distances,method="single"),k=2)
body_sl3## [1] 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2# Die unterschiedlichen Distanzmaße erzeugen durchaus verschiedene Cluster
body_cl2<-cutree(hclust(distances,method="complete"),h=10)
#
body_al2<-cutree(hclust(distances,method="average"),h=7.8)
# eine vergleichende Darstellung der Clusterung über verschiedene Clustering-Methoden
## layout(matrix(c(1,2,3,4,5,6),2,3,byrow=TRUE),c(1,1,1),c(2,1),TRUE)
# plclust(hclust(distances, method="single"), ylab="Height", sub="Single linkage")
# plclust(hclust(distances, method="complete"),ylab="Height", sub="Complete linkage")
# plclust(hclust(distances, method="average"), ylab="Height", sub="Average linkage")
plot(hclust(distances, method="single"), ylab="Height", sub="Single linkage")
plot(hclust(distances, method="complete"),ylab="Height", sub="Complete linkage")
plot(hclust(distances, method="average"), ylab="Height", sub="Average linkage")
# als Darstellungsidee: Plot der beiden principal Components in einem Scatterplot
# die Cluster-Zuordnung kommt aus dem cutree() Befehl
# PCA rechnen und speichern
pc.body<-princomp(d.body,cor=T)
# Plot der Vp-Scores der ersten beiden PCA-Komponenten
# Achsenbereich festlegen
xlim<-range(pc.body$scores[,1])
# Grafik aufmachen
plot(pc.body$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
plot(pc.body$scores[,1:2], type="n")
# An Stelle von Punkten Buchstaben (Clusterzugehörigkeit) an die Koordinaten schreiben
##text(pc.body$scores[,1:2], labels=body_sl3, cex=0.6)
# dito für comlete-linkage
plot(pc.body$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
text(pc.body$scores[,1:2], labels=body_cl2, cex=0.6)
# dito für average-linkage
plot(pc.body$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
text(pc.body$scores[,1:2], labels=body_al2, cex=0.6)
# Einzelgrafik: Zwei principal components plot der 3-Cluster-Lösung mit complete-linkage
##par(mfrow=c(1,1))
##jpeg(file="cl-body-detail.jpg")
c.3 <- hclust(distances, method="complete")
c.3.vp <- cutree(c.3, k=3)
pc<-princomp(d.body,cor=T)
xlim<-range(pc$scores[,1])
plot(pc$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
text(pc$scores[,1:2], labels=c.3.vp, cex=0.8)
##par(mfrow=c(1,1))
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✔ ggplot2 3.3.5 ✔ purrr 0.3.4
## ✔ tibble 3.1.6 ✔ dplyr 1.0.8
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
dd.t <- data.frame(cbind(pc$scores, body_cl2))
dd.t$body_cl2.f <- factor(dd.t$body_cl2)
dd.t %>% ggplot(aes(x=Comp.1, y=Comp.2, group=body_cl2.f, color=body_cl2.f)) +
geom_point()
# d.body wieder aus Namespace nehmen
detach(d.body)Beispiel Lebenserwartung (Everitt, 2010)
Daten von Keyfitz & Flieger (1971). Lebenserwartung nach Geschlecht und Alter getrennt für eine Menge von Ländern (insgesamt 27).
Varianzen:
Birth variance = 66.08
Aged 25 variance = 25.26
Aged 50 variance = 13.07
Aged 75 variance = 4.56Wegen der sehr unterschiedlichen Varianzen bietet sich Standardisierung der Daten an, um die euklidischen Distanzen nicht zu verzerren.
d.life <- read.delim(file="http://md.psych.bio.uni-goettingen.de/mv/data/div/cl-life.txt")
#standardisieren - aber nur die Standardabweichungen (auf 1), die Mittelwerte bleiben.
sds<-apply(d.life[,2:5], 2, sd)
d.st.life <- sweep(as.matrix(d.life[,2:5]),2,sds,FUN="/")
# und zeigen
d.st.life## m0 m25 m50 m75
## [1,] 7.75 10.15 8.30 6.09
## [2,] 4.18 5.77 3.60 2.34
## [3,] 4.67 5.97 4.70 3.28
## [4,] 7.26 8.36 5.53 2.81
## [5,] 6.89 7.56 4.98 3.28
## [6,] 7.63 8.75 6.64 3.28
## [7,] 6.15 7.76 5.53 3.28
## [8,] 8.00 8.75 6.09 3.28
## [9,] 6.89 9.15 6.64 5.15
## [10,] 8.49 9.35 6.64 3.75
## [11,] 8.00 9.55 7.19 4.22
## [12,] 7.87 9.95 7.74 5.15
## [13,] 6.89 8.75 6.91 4.68
## [14,] 7.38 8.75 6.09 2.81
## [15,] 7.50 8.95 6.09 3.75
## [16,] 6.03 7.96 6.09 4.22
## [17,] 7.26 8.36 6.09 2.81
## [18,] 7.75 8.75 6.36 3.75
## [19,] 7.26 8.75 6.64 3.75
## [20,] 8.00 9.55 7.74 6.56
## [21,] 8.00 9.55 7.19 4.22
## [22,] 7.87 8.56 5.81 2.81
## [23,] 8.24 8.95 6.36 3.75
## [24,] 8.00 9.15 6.64 4.22
## [25,] 7.26 8.56 6.36 4.68
## [26,] 7.13 8.75 6.64 4.22
## [27,] 7.01 9.15 7.74 4.22options(digits=3)
#get distance matrix
distances<-dist(d.st.life)
#
#figure 12.6
# nicht unterteiltes Grafikfenster
par(mfrow=c(1,1))
labs <- d.life$country
plot(hclust(distances,method="complete"),ylab="Height",sub="Complete linkage",labels=labs)
# nähere Untersuchung der 4-Cluster Lösung
#pick up 4 group solution
life_cl4<-cutree(hclust(distances,method="complete"),h=3)
#fig 12.7
pairs(d.life[,2:5],panel=function(x,y) text(x,y,labels=life_cl4,cex=0.6))
#Fig 12.8
pc.life <- princomp(d.st.life,cor=T)
xlim <- range(pc.life$scores[,1])
plot(pc.life$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
text(pc.life$scores[,1:2], labels=life_cl4, cex=0.8)
#means and membership of four clusters
# Mittelwerte für die Cluster
country.mean <- lapply(1:4, function(nc) apply(d.life[life_cl4==nc,2:5],2,mean))
country.mean## [[1]]
## m0 m25 m50 m75
## 64.0 49.7 28.7 12.7
##
## [[2]]
## m0 m25 m50 m75
## 36.0 29.5 15.0 6.0
##
## [[3]]
## m0 m25 m50 m75
## 57.75 41.50 20.88 6.75
##
## [[4]]
## m0 m25 m50 m75
## 61.57 45.29 24.29 8.79# die zu den Clustern gehörenden Länder heraussuchen
# ?? noch anpassen
country.clus <- lapply(1:4, function(nc) d.life$country[life_cl4==nc])
country.clus## [[1]]
## [1] "Algeria" "Dominican Rep" "Nicaragua"
##
## [[2]]
## [1] "Cameroon" "Madagascar"
##
## [[3]]
## [1] "Mauritius" "Reunion" "South Africa(C)" "South Africa(W)"
## [5] "Greenland" "Guatemala" "Honduras" "Trinidad (67)"
##
## [[4]]
## [1] "Seychelles" "Tunisia" "Canada"
## [4] "Costa Rica" "El Salvador" "Grenada"
## [7] "Jamaica" "Mexico" "Panama"
## [10] "United States (67)" "Argentina" "Chile"
## [13] "Columbia" "Ecuador"#Beispiel: Kriminalitätsdaten (Everitt, 2010)
Im Beispiel Kriminalitätsdaten USA geht es um eine vorgegebene Anzahl
von Clustern und der Anwendung des Befehls kmeans().
Crime Rates. Quelle: The Statistical Abstract of the USA (1988).
Rates of different types of crime per 100.000 residents.
- murder (Mord)
- rape (Vergewaltigung)
- robbery (Raubüberfall)
- assault (Überfall (mit Körperverletzung?))
- burglery (Einbruch)
- theft (Diebstahl)
# k-means
#crime rate data
#d.crime<-source("c:\\mvmvbs\\chap102_dat.txt")$value
# Daten einlesen
d.crime <- read.delim(file="http://md.psych.bio.uni-goettingen.de/mv/data/div/pca_crime.txt")
head(d.crime)## state murder rape robbery assault burglary theft vehicules
## 1 ME 2.0 14.8 28 102 803 2347 164
## 2 NH 2.2 21.5 24 92 755 2208 228
## 3 VT 2.0 21.8 22 103 949 2697 181
## 4 MA 3.6 29.7 193 331 1071 2189 906
## 5 RI 3.5 21.4 119 192 1294 2568 705
## 6 CT 4.6 23.8 192 205 1198 2758 447#remove DC (ist Ausreisser)
d.crime<-d.crime[-24,]
#rlabs<-row.names(d.crime)
rlabs <- d.crime[,1]
# Varianzen ansehen
apply(d.crime[2:8],2,var)## murder rape robbery assault burglary theft vehicules
## 11.9 209.8 11889.6 19373.5 175895.0 565276.6 43997.4# die sind sehr hoch
# standardize by range
# Ranges ermitteln und speichern
rge <- apply(d.crime[2:8], 2, max) - apply(d.crime[2:8],2,min)
# Standardisieren indem durch Range geteilt wird
crime_std <- sweep(d.crime[2:8], 2, rge, FUN="/")
# Standardisierte Streuungen ansehen
apply(crime_std,2,var)## murder rape robbery assault burglary theft vehicules
## 0.0764 0.0562 0.0463 0.0590 0.0522 0.0622 0.0676# WGSS ermitteln
# within group sum of squares
# Inner-Gruppen-Quadratsumme(n) über die Anzahl der Gruppen
# bei nur einer Gruppe die Varianz in der Gruppe
#plot of wgss against number of clusters
n <- length(crime_std[,1])
# Summe der Varianzen über die Variablen * n-1
wss1 <- (n-1) * sum(apply(crime_std, 2, var))
# einen leeren Vektor aufmachen
wss <- numeric(0)
# und füllen
for(i in 2:6) {
W <- sum(kmeans(crime_std, i)$withinss)
wss<-c(wss, W)
}
# wss1 vorne dran hängen
wss<-c(wss1,wss)
# wss enthält jetzt 6 Werte, die Innergruppen-Quadratsummen
# jetzt plotten
plot(1:6, wss, type="l", xlab="Number of groups", ylab="Within groups sum of squares", lwd=2)
#get two-group solution from k-means and group means and membership
# das Modell rechnen und speichern
crime_kmean2 <- kmeans(crime_std, 2)
# nur die Variablen in einem Datenobjekt speichern
crime <- d.crime[2:8]
# Ausgabe der Mittelwerte unstandardisiert (zum besseren Vergleich)
lapply(1:2, function(nc) apply(crime[crime_kmean2$cluster == nc,], 2, mean))## [[1]]
## murder rape robbery assault burglary theft vehicules
## 9.37 45.37 229.00 394.77 1543.41 3368.05 554.27
##
## [[2]]
## murder rape robbery assault burglary theft vehicules
## 4.74 24.80 73.82 182.07 924.21 2564.71 247.04# Ausgabe der zum Cluster gehörigen Bundesstaaten
# die Werte im Cluster 1 sind deutlich niedriger, als im Cluster 2
lapply(1:2, function(nc) rlabs[crime_kmean2$cluster==nc])## [[1]]
## [1] "MA" "NY" "NJ" "IL" "MI" "MO" "MD" "SC" "GA" "FL" "TN" "LA" "OK" "TX" "CO"
## [16] "NM" "AZ" "NV" "WA" "OR" "CA" "AK"
##
## [[2]]
## [1] "ME" "NH" "VT" "RI" "CT" "PA" "OH" "IN" "WI" "MN" "IA" "ND" "SD" "NE" "KS"
## [16] "DE" "VA" "WV" "NC" "KY" "AL" "MS" "AR" "MT" "ID" "WY" "UT" "HI"# lapply(x, function() ...)
# wendet die function() auf alle Elemente x an
# gibt entsprechend lange Liste von Ergebnissen zurück
# function() ist frei definierbar
# function(nc) übergibt als Paramter nc je ein Element von x, führt function(nc) aus
# und speichert das Ergebnis in ErgebnisvektorBeispiel: Gastroenterologen (Everitt, 2010)
Beurteilt wird die Offenheit von Gastroenterologen in verschiedenen Ländern. Angewendet wird Maximum Likelihood Clustering
Model-Based Clustering: funktioniert auch noch gut bei überlappenden Clustern, wo k-means und agglomeratives Clustern Schwierigkeiten haben. BIC = Basean Information Criterion.
Wie offen sind Gastroenterologen, wenn sie bei einem Patienten Krebs festgestellt haben. Daten von 600 Gastroenterologen aus 27 europäischen Ländern. Ja/Nein (Anteil der Ja).
Q1: Would you tell this patient that he or she has cancer if he or she asks no questions?
Q2: Would you tell the wife or husband that the patient has cancer?
Q3: Would you tell the patient that he or she has a cancer if he or she directly asks you to disclose the diagnosis?
(During surgery, the surgeon notices several small metastases in the liver)
Q4: Would you tell the patient about the metastases (supposing the patient asks to be told the results of the operation)?
Q5: Would you tell the patient that th condition is incurable?
Q6: Would you tell the wife or husband that the operation revealed metastases?d.gastroent <- read.delim(file="http://md.psych.bio.uni-goettingen.de/mv/data/div/cl-gastroent.txt")
#library(mclust02)
library(mclust)## Package 'mclust' version 5.4.10
## Type 'citation("mclust")' for citing this R package in publications.##
## Attache Paket: 'mclust'## Das folgende Objekt ist maskiert 'package:purrr':
##
## mapd.gast <- d.gastroent[2:7]
# das beste Modell finden
c.res<-Mclust(d.gast)
# das beste Modell ausgeben
# hier ist das Basean Information Criterion (BIC) am höchsten
c.res## 'Mclust' model object: (VEV,4)
##
## Available components:
## [1] "call" "data" "modelName" "n"
## [5] "d" "G" "BIC" "loglik"
## [9] "df" "bic" "icl" "hypvol"
## [13] "parameters" "z" "classification" "uncertainty"# die BIC ansehen
c.res$BIC## Bayesian Information Criterion (BIC):
## EII VII EEI VEI EVI VVI EEE VEE EVE VVE EEV
## 1 -107.95 -108.0 -73.543 -73.54 -73.5 -73.5 -9.206 -9.21 -9.21 -9.21 -9.21
## 2 -26.78 -29.0 -17.250 2.85 12.3 21.9 -6.214 11.91 6.83 43.85 4.28
## 3 -5.41 16.6 -11.219 17.02 NA NA -17.312 NA NA NA -12.94
## 4 11.93 25.8 1.980 17.26 NA NA -31.230 NA NA NA NA
## 5 23.26 17.0 -0.287 15.25 NA NA -27.749 NA NA NA NA
## 6 4.21 NA -14.251 NA NA NA -12.493 NA NA NA NA
## 7 8.38 NA 15.421 NA NA NA 5.562 NA NA NA NA
## 8 -12.51 NA 0.150 NA NA NA -0.867 NA NA NA NA
## 9 -26.21 NA -1.167 NA NA NA -15.766 NA NA NA NA
## VEV EVV VVV
## 1 -9.21 -9.21 -9.21
## 2 46.90 -4.99 43.14
## 3 25.93 NA NA
## 4 151.06 NA NA
## 5 NA NA NA
## 6 NA NA NA
## 7 NA NA NA
## 8 NA NA NA
## 9 NA NA NA
##
## Top 3 models based on the BIC criterion:
## VEV,4 VEV,2 VVE,2
## 151.1 46.9 43.8# der höchste steht in
c.res$bic## [1] 151# die Plots dazu
#plot(c.res,d.gast)
plot(c.res)
was bedeuten die Abkürzungen?
aus der Hilfe:
?mclustModelNames
univariateMixture
A vector with the following components:
"E": equal variance (one-dimensional)
"V": variable variance (one-dimensional)
multivariateMixture
A vector with the following components:
"EII": spherical, equal volume
"VII": spherical, unequal volume
"EEI": diagonal, equal volume and shape
"VEI": diagonal, varying volume, equal shape
"EVI": diagonal, equal volume, varying shape
"VVI": diagonal, varying volume and shape
"EEE": ellipsoidal, equal volume, shape, and orientation
"EEV": ellipsoidal, equal volume and equal shape
"VEV": ellipsoidal, equal shape
"VVV": ellipsoidal, varying volume, shape, and orientation
singleComponent
A vector with the following components:
"X": one-dimensional
"XII": spherical
"XXI": diagonal
"XXX": ellipsoidal# Die Mittelwerte der Fragen (Zustimmung zu Frage) in den vier Clustern
c.res$parameters$mean## [,1] [,2] [,3] [,4]
## q1 0.872 0.798 0.2468 0.0429
## q2 0.931 0.779 1.0000 0.9617
## q3 1.000 0.811 0.7941 0.2357
## q4 0.956 0.563 0.2921 0.0640
## q5 0.810 0.306 0.0167 0.0204
## q6 0.919 0.746 1.0000 0.9542countries <- d.gastroent[,1]
#countries in each class
countries[c.res$classification==1]## [1] "Iceland" "Norway" "UK" "Netherlands"countries[c.res$classification==2]## [1] "Sweden" "Finland" "Denmark" "Ireland"
## [5] "Germany" "Switzerland" "Albania" "Czechoslovakia"countries[c.res$classification==3]## [1] "Belgium" "Spain" "Portugal" "Italy" "Greece"
## [6] "Yugoslavia" "Hungary" "Estonia"countries[c.res$classification==4]## [1] "France" "Bulgaria" "Romania" "Poland" "Russia" "Lithuania"
## [7] "Latvia"# der Klassifizierungsvektor
c.res$classification## [1] 1 1 2 2 2 1 2 2 1 3 2 4 3 3 3 3 3 2 4 4 3 2 4 4 4 4 3# und jetzt auch hier Detailabbildung
# mit den ersten beiden PCA-Komponenten und den Clusternummern
par(mfrow=c(1,1))
c.4.vp <- c.res$classification
pc <- princomp(d.gast, corr=T)## Warning: In princomp.default(d.gast, corr = T) :
## zusätzliches Argument 'corr' wird verworfenxlim<-range(pc$scores[,1])
plot(pc$scores[,1:2], type="n", xlim=xlim, ylim=xlim)
text(pc$scores[,1:2], labels=c.4.vp, cex=0.8)
Weitere Beispiele, Übungen / Exercises
An Example from QuantDev
#general packages
library(ggplot2)
library(psych)##
## Attache Paket: 'psych'## Das folgende Objekt ist maskiert 'package:mclust':
##
## sim## Die folgenden Objekte sind maskiert von 'package:ggplot2':
##
## %+%, alpha#cluster packages
library(cluster) #clustering
library(fpc) #flexible procedures for clustering
library(clusterCrit) #cluster criteria
#set filepath for data file
filepath <- "https://quantdev.ssri.psu.edu/sites/qdev/files/AMIBbrief_raw_daily1.csv"
#read in the .csv file using the url() function
daily <- read.csv(file=url(filepath),header=TRUE)
#clean-up of variable names
var.names.daily <- tolower(colnames(daily))
colnames(daily)<-var.names.daily
#creating a new "id" variable
daily$id <- daily$id*10+daily$day
names(daily)## [1] "id" "day" "date" "slphrs" "weath" "lteq" "pss"
## [8] "se" "swls" "evalday" "posaff" "negaff" "temp" "hum"
## [15] "wind" "bar" "prec"#reducing down to variable set
daily <- daily[ ,c("id","slphrs","weath","lteq","pss","se","swls","evalday", "posaff","negaff","temp","hum","wind","bar","prec")]
#names of variables
names(daily)## [1] "id" "slphrs" "weath" "lteq" "pss" "se" "swls"
## [8] "evalday" "posaff" "negaff" "temp" "hum" "wind" "bar"
## [15] "prec"#looking at data
head(daily,10)## id slphrs weath lteq pss se swls evalday posaff negaff temp hum wind
## 1 1010 6.0 1 10 2.50 2 3.8 1 3.9 3.0 28.0 0.79 11.0
## 2 1011 2.0 2 10 2.75 3 4.2 0 3.8 2.3 20.8 0.62 3.6
## 3 1012 9.0 3 10 3.50 4 5.0 1 5.1 1.0 29.1 0.51 1.9
## 4 1013 7.5 2 9 3.00 4 5.0 1 5.6 1.3 30.2 0.58 2.7
## 5 1014 8.0 1 18 2.75 3 4.0 1 4.3 1.1 22.7 0.55 2.4
## 6 1015 8.0 2 19 2.75 3 4.2 1 3.9 1.0 21.4 0.54 0.7
## 7 1016 8.0 3 21 3.50 4 4.6 1 5.1 1.2 31.4 0.49 1.0
## 8 1017 7.0 NA 14 2.75 3 4.6 1 4.8 1.1 45.3 0.52 1.1
## 9 1020 7.0 0 12 3.50 5 5.6 0 6.3 1.4 28.0 0.79 11.0
## 10 1021 6.0 0 20 4.00 5 6.6 0 7.0 1.6 20.8 0.62 3.6
## bar prec
## 1 29.4 0.20
## 2 30.2 0.00
## 3 30.4 0.02
## 4 30.2 0.00
## 5 30.5 0.00
## 6 30.5 0.00
## 7 30.5 0.00
## 8 30.3 0.00
## 9 29.4 0.20
## 10 30.2 0.00#removing observations with NA
dailysub <- daily[complete.cases(daily), ]
describe(dailysub)## vars n mean sd median trimmed mad min max
## id 1 1376 3276.28 1279.88 3271.50 3302.24 1497.43 1010.00 5327.0
## slphrs 2 1376 7.20 1.81 7.00 7.20 1.48 0.00 18.0
## weath 3 1376 2.00 1.29 2.00 2.00 1.48 0.00 4.0
## lteq 4 1376 12.50 10.42 9.00 11.24 8.90 0.00 58.0
## pss 5 1376 2.62 0.68 2.75 2.64 0.74 0.00 4.0
## se 6 1376 3.43 0.99 3.00 3.46 1.48 1.00 5.0
## swls 7 1376 4.11 1.27 4.20 4.15 1.19 1.00 7.0
## evalday 8 1376 0.68 0.46 1.00 0.73 0.00 0.00 1.0
## posaff 9 1376 4.11 1.10 4.20 4.14 1.19 1.00 7.0
## negaff 10 1376 2.45 1.04 2.20 2.34 1.04 1.00 6.9
## temp 11 1376 40.18 7.88 42.00 40.51 8.90 20.80 56.0
## hum 12 1376 0.62 0.20 0.66 0.63 0.21 0.24 0.9
## wind 13 1376 7.36 4.45 7.00 6.81 4.45 0.70 20.0
## bar 14 1376 30.02 0.33 30.00 30.04 0.43 29.32 30.5
## prec 15 1376 0.05 0.09 0.00 0.03 0.00 0.00 0.3
## range skew kurtosis se
## id 4317.00 -0.10 -1.04 34.50
## slphrs 18.00 0.12 1.93 0.05
## weath 4.00 -0.06 -1.06 0.03
## lteq 58.00 1.07 0.95 0.28
## pss 4.00 -0.37 0.17 0.02
## se 4.00 -0.40 -0.12 0.03
## swls 6.00 -0.28 -0.22 0.03
## evalday 1.00 -0.79 -1.37 0.01
## posaff 6.00 -0.24 -0.37 0.03
## negaff 5.90 0.95 0.67 0.03
## temp 35.20 -0.37 -0.24 0.21
## hum 0.66 -0.36 -1.10 0.01
## wind 19.30 0.97 0.86 0.12
## bar 1.22 -0.39 -0.90 0.01
## prec 0.30 1.85 1.98 0.00#scaling all the variables
dailyscale <- data.frame(scale(dailysub, center=TRUE, scale=TRUE))
#checking and fixing the id variable (which we did not want standardized)
str(dailyscale$id)## num [1:1376] -1.77 -1.77 -1.77 -1.77 -1.77 ...dailyscale$id <- dailysub$id
str(dailyscale$id)## num [1:1376] 1010 1011 1012 1013 1014 ...describe(dailyscale)## vars n mean sd median trimmed mad min max range
## id 1 1376 3276 1280 3271.50 3302.24 1497.43 1010.00 5327.00 4317.00
## slphrs 2 1376 0 1 -0.11 0.00 0.82 -3.98 5.98 9.97
## weath 3 1376 0 1 0.00 0.00 1.15 -1.55 1.54 3.09
## lteq 4 1376 0 1 -0.34 -0.12 0.85 -1.20 4.37 5.57
## pss 5 1376 0 1 0.19 0.03 1.08 -3.83 2.02 5.85
## se 6 1376 0 1 -0.43 0.04 1.49 -2.45 1.58 4.03
## swls 7 1376 0 1 0.07 0.03 0.93 -2.45 2.27 4.72
## evalday 8 1376 0 1 0.68 0.10 0.00 -1.47 0.68 2.15
## posaff 9 1376 0 1 0.08 0.03 1.08 -2.82 2.63 5.45
## negaff 10 1376 0 1 -0.24 -0.11 1.00 -1.40 4.28 5.68
## temp 11 1376 0 1 0.23 0.04 1.13 -2.46 2.01 4.47
## hum 12 1376 0 1 0.20 0.05 1.06 -1.94 1.42 3.36
## wind 13 1376 0 1 -0.08 -0.12 1.00 -1.50 2.84 4.33
## bar 14 1376 0 1 -0.05 0.06 1.29 -2.09 1.56 3.65
## prec 15 1376 0 1 -0.53 -0.26 0.00 -0.53 2.68 3.21
## skew kurtosis se
## id -0.10 -1.04 34.50
## slphrs 0.12 1.93 0.03
## weath -0.06 -1.06 0.03
## lteq 1.07 0.95 0.03
## pss -0.37 0.17 0.03
## se -0.40 -0.12 0.03
## swls -0.28 -0.22 0.03
## evalday -0.79 -1.37 0.03
## posaff -0.24 -0.37 0.03
## negaff 0.95 0.67 0.03
## temp -0.37 -0.24 0.03
## hum -0.36 -1.10 0.03
## wind 0.97 0.86 0.03
## bar -0.39 -0.90 0.03
## prec 1.85 1.98 0.03ggplot(dailyscale,aes(x=lteq,y=posaff)) +
geom_point()
data1 <- dailyscale[c(1,3,12),c("id","lteq","posaff")]
head(data1,3)## id lteq posaff
## 1 1010 -0.240 -0.189
## 3 1012 -0.240 0.902
## 14 1025 -0.432 0.538labels.abc <-c("A","B","C")
ggplot(data1,aes(x=lteq,y=posaff)) +
geom_polygon(fill="blue",alpha=.6) +
geom_point(size=3) +
geom_text(aes(x=lteq-.1,label=labels.abc)) +
ylim(-1,1) + xlim(-1,1)
dist.abc <- dist(data1[1:3,2:3],method="euclidean",diag=TRUE,upper=FALSE)
dist.abc## 1 3 14
## 1 0.000
## 3 1.091 0.000
## 14 0.752 0.411 0.000dist.abc2 <- dist(data1[1:3,2:3],method="manhattan",diag=TRUE,upper=FALSE)
dist.abc2## 1 3 14
## 1 0.000
## 3 1.091 0.000
## 14 0.919 0.555 0.000#there are random starts involved so we set a seed
set.seed(1234)
#running a cluster analysis
model <- kmeans(dailyscale[,c("lteq","posaff")], centers=4)
model## K-means clustering with 4 clusters of sizes 377, 578, 240, 181
##
## Cluster means:
## lteq posaff
## 1 -0.656 -1.071
## 2 -0.441 0.700
## 3 0.776 -0.568
## 4 1.744 0.749
##
## Clustering vector:
## 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
## 2 1 2 2 3 3 4 2 4 2 2 2 1 2 2 2
## 20 21 22 23 27 28 29 30 31 32 37 38 39 40 41 42
## 1 1 1 4 1 1 1 1 2 2 2 2 2 2 1 2
## 43 44 47 48 49 51 52 53 54 55 56 57 58 59 60 61
## 2 1 2 2 2 2 2 2 2 1 3 3 1 1 1 3
## 62 63 64 66 67 68 70 71 72 73 74 75 76 77 78 79
## 3 2 4 3 1 3 2 2 2 2 2 2 2 1 2 3
## 81 84 85 86 87 88 89 90 91 92 93 95 96 97 98 99
## 2 1 3 1 2 2 2 4 4 4 4 2 2 2 2 4
## 101 102 103 105 106 107 108 110 111 112 113 114 115 116 117 118
## 4 3 2 3 4 4 3 2 4 4 4 4 4 2 4 4
## 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
## 4 3 1 1 1 1 1 1 1 2 2 2 2 2 2 2
## 135 136 137 138 140 141 143 144 145 146 147 149 150 151 152 153
## 2 4 4 2 3 3 3 4 3 4 4 4 4 4 1 3
## 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
## 2 3 2 3 3 2 2 2 2 2 2 2 2 2 2 2
## 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
## 1 2 3 1 1 1 1 1 1 1 1 2 2 2 3 3
## 186 187 188 189 190 191 192 193 194 196 197 198 199 201 202 203
## 2 4 4 4 3 3 4 1 1 2 2 2 2 2 4 4
## 204 205 206 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 2 4 4 4 2 2 2 2 2 2 1 2 3 3 1
## 221 222 223 224 225 226 228 229 230 231 232 233 234 235 236 237
## 1 3 3 3 3 2 2 2 1 1 2 3 3 2 3 1
## 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253
## 2 2 1 1 3 3 2 3 3 2 3 2 3 3 3 3
## 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
## 3 4 3 3 2 2 2 2 1 2 2 2 2 1 2 1
## 270 271 272 273 274 275 276 277 278 279 280 281 282 283 285 286
## 3 3 2 2 2 2 1 1 1 2 1 1 1 3 3 1
## 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
## 1 2 2 1 1 1 1 1 1 2 2 2 3 1 2 1
## 303 304 305 306 307 308 309 312 313 314 315 316 317 318 319 320
## 3 2 2 2 2 2 1 2 2 2 2 3 3 1 1 2
## 321 323 324 325 326 327 328 329 330 331 332 333 334 335 343 344
## 2 2 2 2 2 2 2 4 2 2 2 2 2 2 3 2
## 345 346 347 348 349 350 352 353 354 355 356 358 359 360 361 364
## 1 2 1 2 2 2 2 2 2 1 1 1 1 2 4 4
## 365 366 367 368 369 370 371 372 373 374 376 377 378 379 380 381
## 4 4 2 2 2 2 3 2 2 3 1 1 1 2 2 1
## 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 1 2 3 2 3 2 2 3 3 3 3 4 1 1 4 3
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 4 4 4 1 1 4 4 3 4 1 1 1 2 1 1 1
## 414 415 416 417 418 419 422 423 424 425 426 427 428 429 430 431
## 1 2 2 2 2 2 1 2 3 3 4 3 3 4 4 2
## 432 433 434 435 436 437 438 439 441 442 443 444 445 446 447 448
## 2 2 2 2 3 1 1 3 2 2 3 3 3 3 2 2
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 2 2 2 1 1 1 1 3 3 1 3 2 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 1 1 2 2 2 1 2 2 3 3 2 1 1 1 1 1
## 481 483 485 486 487 488 489 490 491 492 493 494 495 496 497 498
## 2 1 2 2 2 1 1 1 1 1 1 2 1 2 1 1
## 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514
## 1 1 2 2 3 3 3 3 3 2 2 2 2 2 2 2
## 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530
## 1 1 4 3 2 2 4 2 4 4 1 1 1 2 3 3
## 531 533 534 535 536 537 538 539 540 541 542 543 544 545 546 548
## 3 3 4 4 4 1 1 1 1 1 1 1 4 4 2 4
## 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## 4 2 2 2 4 3 3 4 1 3 4 2 3 1 1 2
## 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
## 3 1 1 2 2 2 2 2 2 2 2 1 3 4 4 4
## 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
## 3 1 1 1 2 2 1 1 2 1 1 2 1 1 1 2
## 597 598 599 601 602 603 604 605 606 607 609 610 611 612 613 614
## 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 1
## 615 616 617 618 619 620 621 622 623 624 625 626 628 629 630 631
## 2 2 2 3 2 2 3 1 1 2 2 2 2 2 2 2
## 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
## 1 1 1 3 1 2 1 1 2 3 2 3 1 1 1 1
## 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
## 1 2 3 1 1 1 3 4 3 1 1 1 1 1 1 3
## 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
## 3 4 4 4 4 4 4 3 4 4 4 2 2 1 4 2
## 680 681 682 684 685 686 687 688 689 690 691 692 693 694 696 697
## 2 2 2 1 3 2 2 4 4 2 2 2 4 4 2 1
## 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713
## 1 2 1 1 1 3 3 3 3 3 3 1 3 1 1 1
## 714 715 716 717 719 720 721 722 723 724 725 726 727 728 731 735
## 2 1 1 1 1 1 3 1 1 1 1 3 4 4 4 2
## 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751
## 4 2 4 4 3 3 3 4 3 3 2 4 3 3 2 2
## 752 753 754 755 757 758 759 760 761 762 763 764 765 766 767 768
## 3 3 2 2 1 2 2 1 1 2 2 1 2 2 2 2
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 2 1 2 2 3 1 3 3 3 1 1 1 3 1 1 1
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 1 1 1 1 2 2 1 1 4 4 4 1 3 2 4 4
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 4 4 4 1 3 1 2 2 2 2 2 2 2 1 1 1
## 817 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
## 2 1 1 1 1 2 2 2 1 2 1 4 1 1 2 2
## 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849
## 1 4 1 2 2 2 1 2 2 2 3 3 3 1 3 2
## 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 866
## 2 1 2 1 3 2 2 4 4 2 4 2 4 4 3 4
## 867 868 869 871 872 873 874 875 876 877 878 879 880 881 882 883
## 3 4 4 3 4 3 4 1 1 4 1 1 2 1 2 1
## 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
## 1 2 2 1 1 1 2 1 2 2 3 3 2 2 1 2
## 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
## 2 2 2 2 2 1 3 1 2 2 3 3 3 1 3 3
## 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931
## 3 3 2 3 2 3 2 1 2 1 2 2 1 2 2 2
## 932 933 934 935 936 937 938 940 942 943 944 945 946 947 948 949
## 1 2 4 4 4 4 4 2 2 2 2 2 1 3 2 2
## 950 951 952 953 956 957 958 959 960 961 962 963 964 965 966 967
## 3 3 2 1 1 1 2 2 2 3 3 3 3 2 3 3
## 968 969 970 971 972 973 974 976 977 978 979 980 982 983 984 985
## 2 1 1 3 4 3 1 2 2 3 3 3 2 2 2 2
## 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## 1 3 3 1 3 3 2 2 4 3 3 3 1 2 3 1
## 1002 1003 1004 1005 1006 1007 1008 1009 1011 1012 1013 1014 1015 1016 1017 1018
## 3 4 3 4 1 2 2 2 1 1 2 3 3 3 4 4
## 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
## 2 2 2 1 3 3 3 4 4 1 2 1 3 1 1 1
## 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
## 1 1 1 2 2 2 2 2 2 2 2 4 2 2 2 2
## 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1064 1065 1066 1067
## 4 2 4 2 2 2 2 1 1 1 1 3 3 1 3 2
## 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083
## 2 3 2 4 2 3 3 3 4 2 2 2 2 1 2 1
## 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099
## 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
## 2 2 1 2 1 1 2 1 2 2 4 2 4 2 2 2
## 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## 2 2 2 3 3 3 1 3 2 2 2 2 2 2 4 4
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
## 4 2 2 4 2 4 4 3 4 4 2 2 2 3 2 2
## 1148 1149 1150 1151 1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165
## 2 2 2 2 1 2 2 1 2 1 2 2 2 1 1 1
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 2 4 4 1 3 1 4 2 4 3 3 2 3 3 4 4
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197
## 1 2 2 1 2 2 3 1 3 3 4 2 2 4 2 4
## 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1209 1210 1211 1212 1213 1215
## 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
## 2 1 2 2 2 2 1 2 1 2 2 1 2 1 4 4
## 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247
## 4 3 4 4 3 3 2 2 1 2 2 2 1 1 2 2
## 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263
## 2 3 1 2 4 2 4 4 2 4 4 4 3 4 2 2
## 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279
## 2 2 3 2 1 3 2 3 4 4 1 2 2 4 2 2
## 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295
## 2 2 1 1 1 1 2 1 1 1 2 2 2 2 2 2
## 1296 1297 1298 1299 1300 1301 1302 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 3 1 3 2 2 2 2 1 1 1 1 2 2 2 2 2
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 1
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 1 1 1 4 1 3 2 3 3 3 3 2 2 2 2 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 2 2 2 2 2 2 2 2 1 2 2 4 4 3 1 4
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 3 3 3 4 1 2 2 4 4 4 4 1 1 1 1 1
## 1393 1394 1395 1396 1397 1398 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
## 1 1 1 3 3 3 2 3 3 4 1 1 2 2 1 2
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425
## 3 2 1 2 2 1 1 1 1 2 1 2 1 1 1 1
## 1426 1427 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 1 2 4 4 4 3 1 3 4 3 1 1 1 1 1 1
## 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458
## 2 1 1 1 1 1 1 1 3 1 2 2 1 3 2 2
##
## Within cluster sum of squares by cluster:
## [1] 201 329 176 180
## (between_SS / total_SS = 67.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#getting centers
model$centers## lteq posaff
## 1 -0.656 -1.071
## 2 -0.441 0.700
## 3 0.776 -0.568
## 4 1.744 0.749#plotting clustered data points with k means
ggplot(dailyscale,aes(x=lteq,y=posaff)) +
geom_point(color=model$cluster, alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=model$centers[1,1],y=model$centers[1,2]),color=1,size=5,shape=18) +
geom_point(aes(x=model$centers[2,1],y=model$centers[2,2]),color=2,size=5,shape=18) +
geom_point(aes(x=model$centers[3,1],y=model$centers[3,2]),color=3,size=5,shape=18) +
geom_point(aes(x=model$centers[4,1],y=model$centers[4,2]),color=4,size=5,shape=18) 
library(animation)
kmeans.ani(dailyscale[,c("lteq","posaff")], centers = 4, pch=c(15,16,17,18), col=c(1,2,3,4))
model$totss## [1] 2750model$withinss## [1] 201 329 176 180model$tot.withinss## [1] 886model$betweenss## [1] 1864#making a empty dataframe
criteria <- data.frame()
#setting range of k
nk <- 1:20
#loop for range of clusters
for (k in nk) {
model <- kmeans(dailyscale[,c("lteq","posaff")], k)
criteria <- rbind(criteria,c(k,model$tot.withinss,model$betweenss,model$totss))
}
#renaming columns
names(criteria) <- c("k","tot.withinss","betweenss","totalss")
#scree plot
ggplot(criteria, aes(x=k)) +
geom_point(aes(y=tot.withinss),color="red") +
geom_line(aes(y=tot.withinss),color="red") +
geom_point(aes(y=betweenss),color="blue") +
geom_line(aes(y=betweenss),color="blue") +
xlab("k = number of clusters") + ylab("Sum of Squares (within = red, between = blue)")
#looking at criteria
round(criteria,2)## k tot.withinss betweenss totalss
## 1 1 2750 0 2750
## 2 2 1789 961 2750
## 3 3 1083 1667 2750
## 4 4 887 1863 2750
## 5 5 714 2036 2750
## 6 6 583 2167 2750
## 7 7 497 2253 2750
## 8 8 466 2284 2750
## 9 9 408 2342 2750
## 10 10 378 2372 2750
## 11 11 340 2410 2750
## 12 12 297 2453 2750
## 13 13 291 2459 2750
## 14 14 283 2467 2750
## 15 15 251 2499 2750
## 16 16 234 2516 2750
## 17 17 217 2533 2750
## 18 18 204 2546 2750
## 19 19 207 2543 2750
## 20 20 186 2564 2750#from library(fpc)
model.manyCH <- kmeansruns(dailyscale[,c("lteq","posaff")], krange=c(2:20), criterion="ch",critout = TRUE, plot=FALSE) #better to leave the plot FALSE## 2 clusters 745
## 3 clusters 1057
## 4 clusters 975
## 5 clusters 978
## 6 clusters 1019
## 7 clusters 1034
## 8 clusters 1017
## 9 clusters 1016
## 10 clusters 1011
## 11 clusters 1014
## 12 clusters 1025
## 13 clusters 1017
## 14 clusters 1008
## 15 clusters 1009
## 16 clusters 1009
## 17 clusters 1016
## 18 clusters 1020
## 19 clusters 1017
## 20 clusters 1019model.manyCH## K-means clustering with 3 clusters of sizes 484, 631, 261
##
## Cluster means:
## lteq posaff
## 1 -0.434 -1.004
## 2 -0.346 0.690
## 3 1.641 0.195
##
## Clustering vector:
## 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
## 1 1 2 2 2 3 3 2 2 2 2 2 1 2 2 2
## 20 21 22 23 27 28 29 30 31 32 37 38 39 40 41 42
## 1 1 1 2 1 1 1 1 2 2 2 2 2 2 1 2
## 43 44 47 48 49 51 52 53 54 55 56 57 58 59 60 61
## 2 1 2 2 2 2 2 2 2 1 3 1 1 1 1 1
## 62 63 64 66 67 68 70 71 72 73 74 75 76 77 78 79
## 3 2 2 1 1 2 2 2 2 2 2 2 2 1 2 2
## 81 84 85 86 87 88 89 90 91 92 93 95 96 97 98 99
## 2 1 1 1 2 2 2 3 3 3 3 2 2 2 2 3
## 101 102 103 105 106 107 108 110 111 112 113 114 115 116 117 118
## 3 3 2 1 3 3 3 2 3 3 3 3 3 2 3 3
## 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
## 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
## 135 136 137 138 140 141 143 144 145 146 147 149 150 151 152 153
## 2 3 3 2 3 2 3 3 2 3 3 3 3 3 1 3
## 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
## 2 2 2 3 2 2 2 2 2 2 2 2 2 1 2 2
## 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
## 1 2 2 1 1 1 1 1 1 1 1 2 2 2 1 2
## 186 187 188 189 190 191 192 193 194 196 197 198 199 201 202 203
## 2 3 3 3 1 3 3 1 1 2 2 2 2 2 3 3
## 204 205 206 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 2 3 3 3 2 2 2 2 2 2 1 2 1 1 1
## 221 222 223 224 225 226 228 229 230 231 232 233 234 235 236 237
## 1 3 1 1 1 2 2 2 1 1 2 2 2 2 1 1
## 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253
## 2 1 1 1 2 2 2 3 3 2 3 2 3 1 3 3
## 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
## 1 3 3 3 2 2 2 2 1 2 2 2 2 1 2 1
## 270 271 272 273 274 275 276 277 278 279 280 281 282 283 285 286
## 3 2 2 2 2 2 1 1 1 2 1 1 1 1 1 1
## 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
## 1 1 2 1 1 1 1 1 1 2 2 2 1 1 2 1
## 303 304 305 306 307 308 309 312 313 314 315 316 317 318 319 320
## 2 2 2 2 2 2 1 2 2 2 2 2 3 1 1 2
## 321 323 324 325 326 327 328 329 330 331 332 333 334 335 343 344
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
## 345 346 347 348 349 350 352 353 354 355 356 358 359 360 361 364
## 1 2 1 2 2 2 2 2 2 1 1 1 1 2 2 3
## 365 366 367 368 369 370 371 372 373 374 376 377 378 379 380 381
## 3 3 2 2 2 2 2 2 2 2 1 1 1 2 2 1
## 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 1 2 1 2 3 2 2 1 1 2 3 3 1 1 3 3
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 3 3 3 1 1 3 3 1 3 1 1 1 2 1 1 1
## 414 415 416 417 418 419 422 423 424 425 426 427 428 429 430 431
## 1 2 2 2 2 2 1 2 3 2 3 3 2 3 3 2
## 432 433 434 435 436 437 438 439 441 442 443 444 445 446 447 448
## 2 2 2 2 2 1 1 3 2 2 1 1 3 3 2 2
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 1 1 2 2 2 1 2 2 3 2 2 1 1 1 1 1
## 481 483 485 486 487 488 489 490 491 492 493 494 495 496 497 498
## 2 1 2 2 2 1 1 1 1 1 1 2 1 2 1 1
## 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514
## 1 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2
## 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530
## 1 1 2 3 2 2 3 2 3 3 1 1 1 2 3 1
## 531 533 534 535 536 537 538 539 540 541 542 543 544 545 546 548
## 3 1 3 3 3 1 1 1 1 1 1 1 2 3 2 3
## 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## 3 2 2 2 3 3 3 3 1 3 3 2 2 1 1 2
## 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
## 3 1 1 2 2 2 2 2 2 2 2 1 3 3 3 3
## 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
## 1 1 1 1 2 2 1 1 2 1 1 2 1 1 1 2
## 597 598 599 601 602 603 604 605 606 607 609 610 611 612 613 614
## 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 1
## 615 616 617 618 619 620 621 622 623 624 625 626 628 629 630 631
## 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2
## 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
## 1 1 1 1 1 2 1 1 2 2 2 1 1 1 1 1
## 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
## 1 2 1 1 1 1 2 3 3 1 1 1 1 1 1 1
## 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
## 3 3 3 3 3 3 3 3 3 3 3 2 2 1 3 2
## 680 681 682 684 685 686 687 688 689 690 691 692 693 694 696 697
## 2 2 2 1 1 2 2 3 3 2 2 2 3 3 2 1
## 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713
## 1 2 1 1 1 1 3 3 3 3 1 1 3 1 1 1
## 714 715 716 717 719 720 721 722 723 724 725 726 727 728 731 735
## 2 1 1 1 1 1 2 1 1 1 1 1 3 3 3 2
## 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751
## 3 2 2 3 1 1 1 3 2 2 2 3 1 3 2 2
## 752 753 754 755 757 758 759 760 761 762 763 764 765 766 767 768
## 1 1 2 2 1 2 1 1 1 2 2 1 2 2 2 2
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 2 1 2 2 1 1 3 1 3 1 1 1 1 1 1 1
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 1 1 1 1 2 2 1 1 3 3 3 1 3 2 3 3
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 3 3 1 3 1 2 2 2 2 2 2 2 1 1 1
## 817 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
## 2 1 1 1 1 2 2 2 1 2 1 3 1 1 2 2
## 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849
## 1 3 1 2 2 2 1 2 2 2 2 1 1 1 3 2
## 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 866
## 2 1 2 1 3 2 2 2 3 2 3 2 3 3 3 3
## 867 868 869 871 872 873 874 875 876 877 878 879 880 881 882 883
## 2 3 3 2 3 3 3 1 1 3 1 1 2 1 2 1
## 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
## 1 2 2 1 1 1 2 1 2 2 2 1 2 2 1 2
## 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
## 2 2 2 2 2 1 1 1 2 2 1 2 1 1 3 3
## 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931
## 1 3 2 2 2 2 1 1 2 1 2 2 1 2 2 2
## 932 933 934 935 936 937 938 940 942 943 944 945 946 947 948 949
## 1 2 3 3 3 3 3 2 2 2 2 2 1 1 1 2
## 950 951 952 953 956 957 958 959 960 961 962 963 964 965 966 967
## 3 2 2 1 1 1 2 2 2 1 1 1 1 2 3 3
## 968 969 970 971 972 973 974 976 977 978 979 980 982 983 984 985
## 2 1 1 3 3 3 1 2 2 3 1 1 2 2 2 1
## 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## 1 3 1 1 2 3 2 2 3 1 3 1 1 2 3 1
## 1002 1003 1004 1005 1006 1007 1008 1009 1011 1012 1013 1014 1015 1016 1017 1018
## 3 3 1 3 1 2 2 2 1 1 2 1 1 3 3 3
## 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
## 2 2 2 1 3 1 2 3 3 1 2 1 1 1 1 1
## 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
## 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1064 1065 1066 1067
## 3 2 3 2 2 2 2 1 1 1 1 2 3 1 1 2
## 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083
## 2 2 2 3 2 3 1 3 3 2 2 2 2 1 2 1
## 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
## 2 2 1 2 1 1 2 1 2 2 3 2 2 2 2 2
## 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## 2 2 2 2 3 3 1 3 2 1 2 2 2 2 3 3
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
## 3 2 2 3 2 3 3 3 3 3 2 2 2 2 2 2
## 1148 1149 1150 1151 1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165
## 2 2 2 2 1 2 2 1 2 1 2 2 2 1 1 1
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 2 3 3 1 1 1 3 2 3 3 1 2 1 2 3 2
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197
## 1 2 2 1 2 2 1 1 1 3 3 1 2 3 2 3
## 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1209 1210 1211 1212 1213 1215
## 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
## 2 1 2 2 2 2 1 2 1 2 2 1 2 1 3 3
## 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247
## 3 3 3 3 1 1 2 2 1 2 2 2 1 1 1 2
## 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263
## 2 2 1 2 3 2 3 2 2 3 3 3 3 3 2 2
## 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279
## 2 2 1 2 1 2 2 2 3 3 1 2 2 3 2 2
## 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295
## 2 2 1 1 1 1 2 1 1 1 2 2 2 2 2 2
## 1296 1297 1298 1299 1300 1301 1302 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 2
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 2 1 2 2 1 2 2 2 2 1 2 2 2 1 2 1
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 1 1 1 3 1 3 2 1 3 3 3 2 2 2 2 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 2 2 2 2 2 2 2 2 1 2 2 3 3 1 1 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 3 3 3 3 1 2 2 3 2 3 2 1 1 1 1 1
## 1393 1394 1395 1396 1397 1398 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
## 1 1 1 3 1 3 2 3 1 3 1 1 2 2 1 2
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425
## 1 2 1 2 2 1 1 1 1 2 1 2 1 1 1 1
## 1426 1427 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 1 2 3 3 3 3 1 3 3 2 1 1 1 1 1 1
## 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458
## 2 1 1 1 1 1 1 1 3 1 2 2 1 1 2 2
##
## Within cluster sum of squares by cluster:
## [1] 335 413 334
## (between_SS / total_SS = 60.6 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "crit"
## [11] "bestk"#another criteria
model.manyASW <- kmeansruns(dailyscale[,c("lteq","posaff")], krange=c(2:20), criterion="asw",critout = TRUE, plot=FALSE) #better to leave the plot FALSE## 2 clusters 0.332
## 3 clusters 0.388
## 4 clusters 0.354
## 5 clusters 0.343
## 6 clusters 0.35
## 7 clusters 0.357
## 8 clusters 0.342
## 9 clusters 0.348
## 10 clusters 0.353
## 11 clusters 0.36
## 12 clusters 0.363
## 13 clusters 0.358
## 14 clusters 0.361
## 15 clusters 0.363
## 16 clusters 0.362
## 17 clusters 0.362
## 18 clusters 0.362
## 19 clusters 0.365
## 20 clusters 0.358model.manyASW## K-means clustering with 3 clusters of sizes 631, 484, 261
##
## Cluster means:
## lteq posaff
## 1 -0.346 0.690
## 2 -0.434 -1.004
## 3 1.641 0.195
##
## Clustering vector:
## 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
## 2 2 1 1 1 3 3 1 1 1 1 1 2 1 1 1
## 20 21 22 23 27 28 29 30 31 32 37 38 39 40 41 42
## 2 2 2 1 2 2 2 2 1 1 1 1 1 1 2 1
## 43 44 47 48 49 51 52 53 54 55 56 57 58 59 60 61
## 1 2 1 1 1 1 1 1 1 2 3 2 2 2 2 2
## 62 63 64 66 67 68 70 71 72 73 74 75 76 77 78 79
## 3 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1
## 81 84 85 86 87 88 89 90 91 92 93 95 96 97 98 99
## 1 2 2 2 1 1 1 3 3 3 3 1 1 1 1 3
## 101 102 103 105 106 107 108 110 111 112 113 114 115 116 117 118
## 3 3 1 2 3 3 3 1 3 3 3 3 3 1 3 3
## 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
## 3 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1
## 135 136 137 138 140 141 143 144 145 146 147 149 150 151 152 153
## 1 3 3 1 3 1 3 3 1 3 3 3 3 3 2 3
## 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
## 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1
## 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
## 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 1
## 186 187 188 189 190 191 192 193 194 196 197 198 199 201 202 203
## 1 3 3 3 2 3 3 2 2 1 1 1 1 1 3 3
## 204 205 206 208 209 210 211 212 213 214 215 216 217 218 219 220
## 1 1 3 3 3 1 1 1 1 1 1 2 1 2 2 2
## 221 222 223 224 225 226 228 229 230 231 232 233 234 235 236 237
## 2 3 2 2 2 1 1 1 2 2 1 1 1 1 2 2
## 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253
## 1 2 2 2 1 1 1 3 3 1 3 1 3 2 3 3
## 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
## 2 3 3 3 1 1 1 1 2 1 1 1 1 2 1 2
## 270 271 272 273 274 275 276 277 278 279 280 281 282 283 285 286
## 3 1 1 1 1 1 2 2 2 1 2 2 2 2 2 2
## 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
## 2 2 1 2 2 2 2 2 2 1 1 1 2 2 1 2
## 303 304 305 306 307 308 309 312 313 314 315 316 317 318 319 320
## 1 1 1 1 1 1 2 1 1 1 1 1 3 2 2 1
## 321 323 324 325 326 327 328 329 330 331 332 333 334 335 343 344
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## 345 346 347 348 349 350 352 353 354 355 356 358 359 360 361 364
## 2 1 2 1 1 1 1 1 1 2 2 2 2 1 1 3
## 365 366 367 368 369 370 371 372 373 374 376 377 378 379 380 381
## 3 3 1 1 1 1 1 1 1 1 2 2 2 1 1 2
## 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 2 1 2 1 3 1 1 2 2 1 3 3 2 2 3 3
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 3 3 3 2 2 3 3 2 3 2 2 2 1 2 2 2
## 414 415 416 417 418 419 422 423 424 425 426 427 428 429 430 431
## 2 1 1 1 1 1 2 1 3 1 3 3 1 3 3 1
## 432 433 434 435 436 437 438 439 441 442 443 444 445 446 447 448
## 1 1 1 1 1 2 2 3 1 1 2 2 3 3 1 1
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 2 2 1 1 1 2 1 1 3 1 1 2 2 2 2 2
## 481 483 485 486 487 488 489 490 491 492 493 494 495 496 497 498
## 1 2 1 1 1 2 2 2 2 2 2 1 2 1 2 2
## 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514
## 2 2 1 1 2 2 2 2 2 1 1 1 1 1 1 1
## 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530
## 2 2 1 3 1 1 3 1 3 3 2 2 2 1 3 2
## 531 533 534 535 536 537 538 539 540 541 542 543 544 545 546 548
## 3 2 3 3 3 2 2 2 2 2 2 2 1 3 1 3
## 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## 3 1 1 1 3 3 3 3 2 3 3 1 1 2 2 1
## 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
## 3 2 2 1 1 1 1 1 1 1 1 2 3 3 3 3
## 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
## 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 1
## 597 598 599 601 602 603 604 605 606 607 609 610 611 612 613 614
## 2 2 2 1 2 2 1 2 2 2 1 1 1 1 2 2
## 615 616 617 618 619 620 621 622 623 624 625 626 628 629 630 631
## 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1
## 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
## 2 2 2 2 2 1 2 2 1 1 1 2 2 2 2 2
## 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
## 2 1 2 2 2 2 1 3 3 2 2 2 2 2 2 2
## 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
## 3 3 3 3 3 3 3 3 3 3 3 1 1 2 3 1
## 680 681 682 684 685 686 687 688 689 690 691 692 693 694 696 697
## 1 1 1 2 2 1 1 3 3 1 1 1 3 3 1 2
## 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713
## 2 1 2 2 2 2 3 3 3 3 2 2 3 2 2 2
## 714 715 716 717 719 720 721 722 723 724 725 726 727 728 731 735
## 1 2 2 2 2 2 1 2 2 2 2 2 3 3 3 1
## 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751
## 3 1 1 3 2 2 2 3 1 1 1 3 2 3 1 1
## 752 753 754 755 757 758 759 760 761 762 763 764 765 766 767 768
## 2 2 1 1 2 1 2 2 2 1 1 2 1 1 1 1
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 1 2 1 1 2 2 3 2 3 2 2 2 2 2 2 2
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 2 2 2 2 1 1 2 2 3 3 3 2 3 1 3 3
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 3 3 2 3 2 1 1 1 1 1 1 1 2 2 2
## 817 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
## 1 2 2 2 2 1 1 1 2 1 2 3 2 2 1 1
## 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849
## 2 3 2 1 1 1 2 1 1 1 1 2 2 2 3 1
## 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 866
## 1 2 1 2 3 1 1 1 3 1 3 1 3 3 3 3
## 867 868 869 871 872 873 874 875 876 877 878 879 880 881 882 883
## 1 3 3 1 3 3 3 2 2 3 2 2 1 2 1 2
## 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
## 2 1 1 2 2 2 1 2 1 1 1 2 1 1 2 1
## 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
## 1 1 1 1 1 2 2 2 1 1 2 1 2 2 3 3
## 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931
## 2 3 1 1 1 1 2 2 1 2 1 1 2 1 1 1
## 932 933 934 935 936 937 938 940 942 943 944 945 946 947 948 949
## 2 1 3 3 3 3 3 1 1 1 1 1 2 2 2 1
## 950 951 952 953 956 957 958 959 960 961 962 963 964 965 966 967
## 3 1 1 2 2 2 1 1 1 2 2 2 2 1 3 3
## 968 969 970 971 972 973 974 976 977 978 979 980 982 983 984 985
## 1 2 2 3 3 3 2 1 1 3 2 2 1 1 1 2
## 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## 2 3 2 2 1 3 1 1 3 2 3 2 2 1 3 2
## 1002 1003 1004 1005 1006 1007 1008 1009 1011 1012 1013 1014 1015 1016 1017 1018
## 3 3 2 3 2 1 1 1 2 2 1 2 2 3 3 3
## 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
## 1 1 1 2 3 2 1 3 3 2 1 2 2 2 2 2
## 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
## 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1064 1065 1066 1067
## 3 1 3 1 1 1 1 2 2 2 2 1 3 2 2 1
## 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083
## 1 1 1 3 1 3 2 3 3 1 1 1 1 2 1 2
## 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
## 1 1 2 1 2 2 1 2 1 1 3 1 1 1 1 1
## 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## 1 1 1 1 3 3 2 3 1 2 1 1 1 1 3 3
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
## 3 1 1 3 1 3 3 3 3 3 1 1 1 1 1 1
## 1148 1149 1150 1151 1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165
## 1 1 1 1 2 1 1 2 1 2 1 1 1 2 2 2
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 1 3 3 2 2 2 3 1 3 3 2 1 2 1 3 1
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197
## 2 1 1 2 1 1 2 2 2 3 3 2 1 3 1 3
## 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1209 1210 1211 1212 1213 1215
## 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
## 1 2 1 1 1 1 2 1 2 1 1 2 1 2 3 3
## 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247
## 3 3 3 3 2 2 1 1 2 1 1 1 2 2 2 1
## 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263
## 1 1 2 1 3 1 3 1 1 3 3 3 3 3 1 1
## 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279
## 1 1 2 1 2 1 1 1 3 3 2 1 1 3 1 1
## 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295
## 1 1 2 2 2 2 1 2 2 2 1 1 1 1 1 1
## 1296 1297 1298 1299 1300 1301 1302 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 1
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 1 2 1 1 2 1 1 1 1 2 1 1 1 2 1 2
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 2 2 2 3 2 3 1 2 3 3 3 1 1 1 1 1
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 1 1 1 1 1 1 1 1 2 1 1 3 3 2 2 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 3 3 3 3 2 1 1 3 1 3 1 2 2 2 2 2
## 1393 1394 1395 1396 1397 1398 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
## 2 2 2 3 2 3 1 3 2 3 2 2 1 1 2 1
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425
## 2 1 2 1 1 2 2 2 2 1 2 1 2 2 2 2
## 1426 1427 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 2 1 3 3 3 3 2 3 3 1 2 2 2 2 2 2
## 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458
## 1 2 2 2 2 2 2 2 3 2 1 1 2 2 1 1
##
## Within cluster sum of squares by cluster:
## [1] 413 335 334
## (between_SS / total_SS = 60.6 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault" "crit"
## [11] "bestk"#obtaining distance matrix
dist.all <- dist(dailyscale[,c("lteq","posaff")],method="euclidean",diag=TRUE,upper=FALSE)
#obtaining metrics
cluster.stats(dist.all,clustering=model$cluster)## $n
## [1] 1376
##
## $cluster.number
## [1] 20
##
## $cluster.size
## [1] 66 49 94 43 32 100 62 16 25 118 116 39 12 63 110 76 91 53 129
## [20] 82
##
## $min.cluster.size
## [1] 12
##
## $noisen
## [1] 0
##
## $diameter
## [1] 1.480 1.480 0.858 1.251 2.347 0.883 1.482 1.667 1.947 1.028 1.057 1.445
## [13] 2.432 1.242 0.976 0.990 1.021 1.538 0.927 0.937
##
## $average.distance
## [1] 0.601 0.507 0.353 0.434 0.785 0.353 0.523 0.673 0.699 0.421 0.406 0.566
## [13] 1.154 0.525 0.364 0.458 0.402 0.465 0.380 0.354
##
## $median.distance
## [1] 0.578 0.454 0.340 0.411 0.665 0.340 0.488 0.542 0.678 0.396 0.394 0.545
## [13] 1.034 0.499 0.364 0.454 0.394 0.454 0.364 0.340
##
## $separation
## [1] 0.0960 0.0909 0.0909 0.0960 0.1322 0.0682 0.0909 0.1818 0.1322 0.0909
## [11] 0.0909 0.0909 0.3019 0.0960 0.0682 0.0909 0.0909 0.0909 0.0909 0.0909
##
## $average.toother
## [1] 2.27 2.21 1.79 1.95 3.10 1.40 2.44 2.75 2.61 1.77 1.47 2.13 3.52 1.86 1.38
## [16] 1.75 1.65 2.17 1.61 1.64
##
## $separation.matrix
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
## [1,] 0.000 1.9755 1.8789 0.206 0.132 0.9975 2.4495 0.617 0.132 1.9310 0.0960
## [2,] 1.975 0.0000 2.0807 1.122 3.040 1.6132 0.1919 0.998 2.947 0.5518 1.0403
## [3,] 1.879 2.0807 0.0000 1.784 2.687 0.0909 1.9086 2.878 1.786 0.9088 0.8921
## [4,] 0.206 1.1218 1.7841 0.000 1.000 0.9416 1.8059 0.182 1.216 1.4422 0.0960
## [5,] 0.132 3.0398 2.6868 1.000 0.000 1.8591 3.5925 1.439 0.132 3.0598 1.2324
## [6,] 0.998 1.6132 0.0909 0.942 1.859 0.0000 1.6178 2.053 1.188 0.6166 0.0909
## [7,] 2.450 0.1919 1.9086 1.806 3.592 1.6178 0.0000 2.023 3.368 0.0909 1.3911
## [8,] 0.617 0.9975 2.8784 0.182 1.439 2.0532 2.0233 0.000 2.036 2.3315 1.1513
## [9,] 0.132 2.9466 1.7860 1.216 0.132 1.1881 3.3685 2.036 0.000 2.5955 0.9274
## [10,] 1.931 0.5518 0.9088 1.442 3.060 0.6166 0.0909 2.331 2.596 0.0000 0.8494
## [11,] 0.096 1.0403 0.8921 0.096 1.232 0.0909 1.3911 1.151 0.927 0.8494 0.0000
## [12,] 0.927 2.7417 0.7335 1.618 1.299 0.5453 2.8762 2.671 0.264 1.8966 0.8180
## [13,] 0.302 2.2913 3.3596 0.425 0.411 2.5033 3.1777 0.464 1.657 3.0706 1.5728
## [14,] 0.904 0.1322 1.6138 0.132 1.980 0.9035 0.7889 0.488 1.890 0.8494 0.1818
## [15,] 1.149 0.9088 0.5781 0.583 2.264 0.0682 0.9483 1.539 1.789 0.0909 0.0909
## [16,] 0.096 2.0554 0.9639 0.636 0.773 0.1919 2.3339 1.644 0.192 1.4669 0.0909
## [17,] 1.335 0.0909 1.2752 0.725 2.485 0.7952 0.2123 1.546 2.244 0.0909 0.2643
## [18,] 1.963 2.7417 0.0909 2.178 2.482 0.5781 2.6356 3.300 1.442 1.6359 1.3211
## [19,] 1.823 1.3143 0.0909 1.509 2.761 0.0909 1.0906 2.548 2.043 0.0909 0.7676
## [20,] 1.116 2.2721 0.0909 1.281 1.823 0.0909 2.2559 2.390 0.937 1.2423 0.4111
## [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.9274 0.302 0.904 1.1492 0.0960 1.3353 1.9628 1.8232 1.1164
## [2,] 2.7417 2.291 0.132 0.9088 2.0554 0.0909 2.7417 1.3143 2.2721
## [3,] 0.7335 3.360 1.614 0.5781 0.9639 1.2752 0.0909 0.0909 0.0909
## [4,] 1.6178 0.425 0.132 0.5829 0.6362 0.7249 2.1781 1.5094 1.2809
## [5,] 1.2993 0.411 1.980 2.2640 0.7730 2.4850 2.4818 2.7611 1.8232
## [6,] 0.5453 2.503 0.904 0.0682 0.1919 0.7952 0.5781 0.0909 0.0909
## [7,] 2.8762 3.178 0.789 0.9483 2.3339 0.2123 2.6356 1.0906 2.2559
## [8,] 2.6712 0.464 0.488 1.5392 1.6443 1.5460 3.2996 2.5481 2.3905
## [9,] 0.2643 1.657 1.890 1.7890 0.1919 2.2435 1.4422 2.0427 0.9370
## [10,] 1.8966 3.071 0.849 0.0909 1.4669 0.0909 1.6359 0.0909 1.2423
## [11,] 0.8180 1.573 0.182 0.0909 0.0909 0.2643 1.3211 0.7676 0.4111
## [12,] 0.0000 2.539 1.909 1.2160 0.0909 1.9182 0.1919 1.1895 0.0909
## [13,] 2.5392 0.000 1.361 2.2145 1.7396 2.3029 3.5842 3.1555 2.6762
## [14,] 1.9086 1.361 0.000 0.1818 1.0709 0.0960 2.1780 1.1037 1.4667
## [15,] 1.2160 2.214 0.182 0.0000 0.6608 0.0909 1.1970 0.0909 0.7271
## [16,] 0.0909 1.740 1.071 0.6608 0.0000 1.2423 0.9056 1.0594 0.0960
## [17,] 1.9182 2.303 0.096 0.0909 1.2423 0.0000 1.9182 0.5379 1.4541
## [18,] 0.1919 3.584 2.178 1.1970 0.9056 1.9182 0.0000 0.8180 0.0909
## [19,] 1.1895 3.155 1.104 0.0909 1.0594 0.5379 0.8180 0.0000 0.4637
## [20,] 0.0909 2.676 1.467 0.7271 0.0960 1.4541 0.0909 0.4637 0.0000
##
## $ave.between.matrix
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0.00 2.919 2.878 1.064 1.25 2.018 3.534 1.86 1.48 2.978 1.412 2.055 1.89
## [2,] 2.92 0.000 2.821 2.000 4.01 2.339 0.919 2.15 3.94 1.403 2.015 3.595 3.50
## [3,] 2.88 2.821 0.000 2.715 3.68 0.941 2.756 3.75 2.76 1.606 1.694 1.664 4.52
## [4,] 1.06 2.000 2.715 0.000 2.09 1.834 2.665 1.20 2.27 2.317 1.088 2.464 1.97
## [5,] 1.25 4.014 3.683 2.094 0.00 2.905 4.638 2.68 1.38 4.037 2.421 2.442 2.07
## [6,] 2.02 2.339 0.941 1.834 2.90 0.000 2.522 2.90 2.17 1.484 0.833 1.388 3.64
## [7,] 3.53 0.919 2.756 2.665 4.64 2.522 0.000 2.92 4.40 1.197 2.430 3.853 4.26
## [8,] 1.86 2.148 3.755 1.196 2.68 2.904 2.917 0.00 3.23 3.004 2.157 3.582 1.63
## [9,] 1.48 3.937 2.762 2.269 1.38 2.173 4.398 3.23 0.00 3.541 2.016 1.330 3.04
## [10,] 2.98 1.403 1.606 2.317 4.04 1.484 1.197 3.00 3.54 0.000 1.668 2.809 4.16
## [11,] 1.41 2.015 1.694 1.088 2.42 0.833 2.430 2.16 2.02 1.668 0.000 1.694 2.90
## [12,] 2.05 3.595 1.664 2.464 2.44 1.388 3.853 3.58 1.33 2.809 1.694 0.000 3.83
## [13,] 1.89 3.501 4.523 1.970 2.07 3.636 4.261 1.63 3.04 4.159 2.904 3.832 0.00
## [14,] 1.89 1.161 2.552 0.994 2.97 1.806 1.811 1.43 2.98 1.673 1.220 2.847 2.63
## [15,] 2.17 1.640 1.325 1.649 3.20 0.781 1.824 2.56 2.70 0.912 0.857 2.072 3.53
## [16,] 1.29 2.886 1.758 1.586 1.98 1.041 3.270 2.70 1.26 2.375 0.949 0.974 3.05
## [17,] 2.50 0.935 1.974 1.718 3.59 1.505 1.159 2.32 3.29 0.788 1.330 2.796 3.52
## [18,] 2.96 3.545 0.881 3.059 3.55 1.357 3.553 4.17 2.45 2.403 2.062 1.249 4.71
## [19,] 2.78 2.150 0.766 2.389 3.73 0.896 2.059 3.32 3.00 0.927 1.457 2.084 4.26
## [20,] 2.15 2.890 0.885 2.199 2.87 0.637 3.050 3.31 1.94 1.965 1.219 0.951 3.88
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 1.889 2.174 1.291 2.496 2.959 2.782 2.150
## [2,] 1.161 1.640 2.886 0.935 3.545 2.150 2.890
## [3,] 2.552 1.325 1.758 1.974 0.881 0.766 0.885
## [4,] 0.994 1.649 1.586 1.718 3.059 2.389 2.199
## [5,] 2.969 3.203 1.978 3.591 3.548 3.731 2.869
## [6,] 1.806 0.781 1.041 1.505 1.357 0.896 0.637
## [7,] 1.811 1.824 3.270 1.159 3.553 2.059 3.050
## [8,] 1.430 2.557 2.697 2.323 4.169 3.321 3.313
## [9,] 2.976 2.699 1.256 3.291 2.448 3.004 1.938
## [10,] 1.673 0.912 2.375 0.788 2.403 0.927 1.965
## [11,] 1.220 0.857 0.949 1.330 2.062 1.457 1.219
## [12,] 2.847 2.072 0.974 2.796 1.249 2.084 0.951
## [13,] 2.630 3.535 3.050 3.518 4.715 4.263 3.882
## [14,] 0.000 1.291 2.035 1.014 3.110 2.032 2.313
## [15,] 1.291 0.000 1.543 0.819 1.968 0.829 1.307
## [16,] 2.035 1.543 0.000 2.168 1.742 1.870 0.971
## [17,] 1.014 0.819 2.168 0.000 2.687 1.332 2.050
## [18,] 3.110 1.968 1.742 2.687 0.000 1.541 0.925
## [19,] 2.032 0.829 1.870 1.332 1.541 0.000 1.220
## [20,] 2.313 1.307 0.971 2.050 0.925 1.220 0.000
##
## $average.between
## [1] 1.84
##
## $average.within
## [1] 0.449
##
## $n.between
## [1] 887420
##
## $n.within
## [1] 58580
##
## $max.diameter
## [1] 2.43
##
## $min.separation
## [1] 0.0682
##
## $within.cluster.ss
## [1] 186
##
## $clus.avg.silwidths
## 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0.299 0.339 0.428 0.457 0.277 0.320 0.373 0.391 0.290 0.357 0.378 0.261 0.178
## 14 15 16 17 18 19 20
## 0.316 0.369 0.359 0.338 0.374 0.356 0.363
##
## $avg.silwidth
## [1] 0.353
##
## $g2
## NULL
##
## $g3
## NULL
##
## $pearsongamma
## [1] 0.358
##
## $dunn
## [1] 0.028
##
## $dunn2
## [1] 0.552
##
## $entropy
## [1] 2.86
##
## $wb.ratio
## [1] 0.243
##
## $ch
## [1] 985
##
## $cwidegap
## [1] 0.206 0.454 0.288 0.212 0.815 0.192 0.288 0.678 1.028 0.288 0.182 0.464
## [13] 0.667 0.227 0.192 0.132 0.192 0.681 0.288 0.192
##
## $widestgap
## [1] 1.03
##
## $sindex
## [1] 0.0901
##
## $corrected.rand
## NULL
##
## $vi
## NULL#library(clusterCrit)
#running a cluster analysis
model <- kmeans(dailyscale[,c("lteq","posaff")], centers=4)
#calculating various internal clustering validation or quality criteria
ic <- intCriteria(traj=as.matrix(dailyscale[,c("lteq","posaff")]), part=model$cluster, crit="all")
ic## $ball_hall
## [1] 0.715
##
## $banfeld_raftery
## [1] -703
##
## $c_index
## [1] 0.114
##
## $calinski_harabasz
## [1] 975
##
## $davies_bouldin
## [1] 0.968
##
## $det_ratio
## [1] 10.7
##
## $dunn
## [1] 0.0174
##
## $gamma
## [1] 0.718
##
## $g_plus
## [1] 0.0556
##
## $gdi11
## [1] 0.0174
##
## $gdi12
## [1] 0.133
##
## $gdi13
## [1] 0.0469
##
## $gdi21
## [1] 0.683
##
## $gdi22
## [1] 5.24
##
## $gdi23
## [1] 1.84
##
## $gdi31
## [1] 0.274
##
## $gdi32
## [1] 2.1
##
## $gdi33
## [1] 0.739
##
## $gdi41
## [1] 0.225
##
## $gdi42
## [1] 1.72
##
## $gdi43
## [1] 0.606
##
## $gdi51
## [1] 0.119
##
## $gdi52
## [1] 0.913
##
## $gdi53
## [1] 0.321
##
## $ksq_detw
## [1] 2799085
##
## $log_det_ratio
## [1] 3257
##
## $log_ss_ratio
## [1] 0.757
##
## $mcclain_rao
## [1] 0.463
##
## $pbm
## [1] 1.52
##
## $point_biserial
## [1] -0.489
##
## $ray_turi
## [1] 0.464
##
## $ratkowsky_lance
## [1] 0.413
##
## $scott_symons
## [1] -3555
##
## $sd_scat
## [1] 0.379
##
## $sd_dis
## [1] 1.63
##
## $s_dbw
## [1] 5.12
##
## $silhouette
## [1] 0.343
##
## $tau
## [1] 0.451
##
## $trace_w
## [1] 878
##
## $trace_wib
## [1] 4.82
##
## $wemmert_gancarski
## [1] 0.493
##
## $xie_beni
## [1] 77.2#kmeans with nstart = 1
km.res <- kmeans(dailyscale[,c("lteq","posaff")], centers=4, nstart = 1)
km.res$tot.withinss## [1] 878#kmeans with nstart = 25
km.res <- kmeans(dailyscale[,c("lteq","posaff")], centers=4, nstart = 25)
km.res$tot.withinss## [1] 878#kmeans with nstart = 50
km.res <- kmeans(dailyscale[,c("lteq","posaff")], centers=4, nstart = 50)
km.res$tot.withinss## [1] 878dailyscale.clus <- cbind(km.res$cluster,dailyscale)
names(dailyscale.clus)[1] <- "cluster"
head(dailyscale.clus[,c(1:4,6)],4)## cluster id slphrs weath pss
## 1 4 1010 -0.662 -0.773250 -0.173
## 2 4 1011 -2.877 -0.000562 0.192
## 3 2 1012 0.999 0.772127 1.289
## 4 2 1013 0.168 -0.000562 0.558library(tidyverse)
# Gather the data to 'long' format so the clustering variables are all in one column
#gather() has been replaced by pivot_longer()
longdata <- dailyscale.clus %>%
pivot_longer(c(lteq, posaff), names_to = "variable", values_to = "value")
# Create the summary statistics seperately for cluster and variable (i.e. lteq, posaff)
summary <- longdata %>%
group_by(cluster, variable) %>%
summarise(mean = mean(value), se = sd(value) / length(value))## `summarise()` has grouped output by 'cluster'. You can override using the
## `.groups` argument.# Plot
ggplot(summary, aes(x = variable, y = mean, fill = variable)) +
geom_bar(stat = 'identity', position = 'dodge') +
geom_errorbar(aes(ymin = mean - se, ymax = mean + se),
width = 0.2,
position = position_dodge(0.9)) +
facet_wrap(~cluster) 
## Analyzing the Cluseters
fit1 <- aov(pss ~ factor(km.res$cluster), data=dailyscale.clus)
summary(fit1)## Df Sum Sq Mean Sq F value Pr(>F)
## factor(km.res$cluster) 3 247 82.3 100 <2e-16 ***
## Residuals 1372 1128 0.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(fit1) ## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = pss ~ factor(km.res$cluster), data = dailyscale.clus)
##
## $`factor(km.res$cluster)`
## diff lwr upr p adj
## 2-1 0.48604 0.277 0.696 0.000
## 3-1 0.49370 0.281 0.706 0.000
## 4-1 -0.44387 -0.649 -0.239 0.000
## 3-2 0.00767 -0.163 0.179 0.999
## 4-2 -0.92990 -1.092 -0.768 0.000
## 4-3 -0.93757 -1.103 -0.772 0.000## Hierarchical Clustering
dist.all <- daisy(dailyscale[,c("lteq","posaff")],metric="euclidean",stand=FALSE)
#loking at distances among first 5 persons
as.matrix(dist.all)[1:5,1:5]## 1 2 3 4 5
## 1 0.0000 0.0909 1.091 1.548 0.849
## 2 0.0909 0.0000 1.181 1.639 0.892
## 3 1.0906 1.1815 0.000 0.464 1.057
## 4 1.5480 1.6387 0.464 0.000 1.463
## 5 0.8494 0.8921 1.057 1.463 0.000# Compute Ward clusters for IGother
clusterward.papa <- agnes(dist.all, diss = TRUE, method = "ward")
# Plot
layout(matrix(1))
plot(clusterward.papa, which.plot = 2, main = "Ward clustering of PAPA")
wardcluster4 <- cutree(clusterward.papa, k = 4)
cluster.stats(dist.all, clustering=wardcluster4,
silhouette = TRUE, sepindex = TRUE)## $n
## [1] 1376
##
## $cluster.number
## [1] 4
##
## $cluster.size
## [1] 437 443 229 267
##
## $min.cluster.size
## [1] 229
##
## $noisen
## [1] 0
##
## $diameter
## [1] 4.71 3.03 4.36 2.84
##
## $average.distance
## [1] 1.071 0.873 1.291 0.876
##
## $median.distance
## [1] 0.964 0.858 1.204 0.815
##
## $separation
## [1] 0.0909 0.0909 0.0909 0.0909
##
## $average.toother
## [1] 1.78 1.97 2.40 2.16
##
## $separation.matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.0000 0.0909 0.0909 0.0909
## [2,] 0.0909 0.0000 0.0960 0.0909
## [3,] 0.0909 0.0960 0.0000 1.6532
## [4,] 0.0909 0.0909 1.6532 0.0000
##
## $ave.between.matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.00 1.72 2.02 1.66
## [2,] 1.72 0.00 2.27 2.11
## [3,] 2.02 2.27 0.00 3.23
## [4,] 1.66 2.11 3.23 0.00
##
## $average.between
## [1] 2.04
##
## $average.within
## [1] 1.01
##
## $n.between
## [1] 691214
##
## $n.within
## [1] 254786
##
## $max.diameter
## [1] 4.71
##
## $min.separation
## [1] 0.0909
##
## $within.cluster.ss
## [1] 948
##
## $clus.avg.silwidths
## 1 2 3 4
## 0.178 0.453 0.283 0.452
##
## $avg.silwidth
## [1] 0.338
##
## $g2
## NULL
##
## $g3
## NULL
##
## $pearsongamma
## [1] 0.483
##
## $dunn
## [1] 0.0193
##
## $dunn2
## [1] 1.28
##
## $entropy
## [1] 1.35
##
## $wb.ratio
## [1] 0.494
##
## $ch
## [1] 869
##
## $cwidegap
## [1] 0.725 0.617 0.909 0.454
##
## $widestgap
## [1] 0.909
##
## $sindex
## [1] 0.129
##
## $corrected.rand
## NULL
##
## $vi
## NULL## K-medoids
# Compute PAM clustering solution for k=4
clusterpam.papa <- pam(dist.all, k=4, diss = TRUE)
clusterpam.papa## Medoids:
## ID
## [1,] "129" "154"
## [2,] "108" "130"
## [3,] "676" "739"
## [4,] "233" "262"
## Clustering vector:
## 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
## 1 1 2 2 3 3 3 2 2 2 2 2 4 2 1 2
## 20 21 22 23 27 28 29 30 31 32 37 38 39 40 41 42
## 1 4 4 2 4 4 4 4 2 1 1 1 2 2 4 2
## 43 44 47 48 49 51 52 53 54 55 56 57 58 59 60 61
## 2 1 1 1 1 1 2 1 1 4 3 4 4 4 4 4
## 62 63 64 66 67 68 70 71 72 73 74 75 76 77 78 79
## 3 1 2 3 4 1 2 2 2 1 2 2 1 1 2 1
## 81 84 85 86 87 88 89 90 91 92 93 95 96 97 98 99
## 1 1 4 1 1 2 2 3 3 3 3 2 2 2 2 3
## 101 102 103 105 106 107 108 110 111 112 113 114 115 116 117 118
## 3 3 2 4 3 3 3 2 3 3 3 3 3 3 3 3
## 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
## 3 4 1 4 4 4 4 4 1 2 2 2 2 1 2 2
## 135 136 137 138 140 141 143 144 145 146 147 149 150 151 152 153
## 2 3 3 2 3 1 3 3 1 3 3 3 3 3 4 3
## 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
## 1 1 1 3 3 2 2 2 2 2 2 2 1 1 2 2
## 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
## 1 1 1 4 1 4 4 4 4 1 1 1 2 2 4 1
## 186 187 188 189 190 191 192 193 194 196 197 198 199 201 202 203
## 1 3 3 3 1 3 3 4 4 2 1 1 1 1 3 3
## 204 205 206 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 2 3 3 3 1 2 2 1 1 1 1 2 4 4 4
## 221 222 223 224 225 226 228 229 230 231 232 233 234 235 236 237
## 4 3 4 4 4 2 2 2 4 4 1 3 1 1 1 4
## 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253
## 1 1 1 4 1 1 2 3 3 1 3 2 3 1 3 3
## 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
## 4 3 3 3 2 1 2 2 4 1 1 2 1 1 1 1
## 270 271 272 273 274 275 276 277 278 279 280 281 282 283 285 286
## 3 1 1 1 1 2 1 1 1 1 1 1 4 1 4 4
## 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
## 4 1 2 1 1 1 4 1 4 2 2 2 1 1 1 4
## 303 304 305 306 307 308 309 312 313 314 315 316 317 318 319 320
## 1 2 2 2 1 2 1 1 2 2 1 1 3 4 4 2
## 321 323 324 325 326 327 328 329 330 331 332 333 334 335 343 344
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2
## 345 346 347 348 349 350 352 353 354 355 356 358 359 360 361 364
## 1 1 1 1 1 2 1 2 1 1 1 1 1 2 2 3
## 365 366 367 368 369 370 371 372 373 374 376 377 378 379 380 381
## 3 3 2 1 1 1 1 1 1 1 4 4 4 2 2 4
## 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 4 1 4 1 3 1 1 1 1 1 3 3 4 4 3 3
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 3 3 3 1 4 3 3 1 3 4 4 1 1 4 4 4
## 414 415 416 417 418 419 422 423 424 425 426 427 428 429 430 431
## 4 2 1 2 2 2 1 2 3 1 3 3 3 3 3 2
## 432 433 434 435 436 437 438 439 441 442 443 444 445 446 447 448
## 2 2 1 1 1 1 1 3 2 1 1 4 3 3 2 2
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 1 2 2 4 4 4 4 4 4 4 4 1 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 1 1 1 1 1 4 2 1 3 3 1 1 1 4 4 4
## 481 483 485 486 487 488 489 490 491 492 493 494 495 496 497 498
## 2 4 2 1 2 4 4 1 4 4 4 2 1 2 1 1
## 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514
## 4 4 1 3 1 4 4 4 4 1 2 2 2 2 2 2
## 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530
## 4 1 2 3 2 2 3 2 3 3 4 1 1 2 3 1
## 531 533 534 535 536 537 538 539 540 541 542 543 544 545 546 548
## 3 4 3 3 3 4 4 4 4 4 4 4 2 3 2 3
## 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## 3 2 2 1 3 3 3 3 4 3 3 2 3 4 1 2
## 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
## 3 4 1 2 2 2 2 2 2 2 2 4 3 3 3 3
## 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
## 4 4 4 1 2 1 1 1 1 1 1 2 1 4 4 1
## 597 598 599 601 602 603 604 605 606 607 609 610 611 612 613 614
## 1 4 4 1 1 4 1 4 4 4 2 1 1 2 1 4
## 615 616 617 618 619 620 621 622 623 624 625 626 628 629 630 631
## 1 2 1 1 2 2 1 4 1 2 2 1 2 2 1 1
## 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
## 4 1 4 4 1 2 4 4 1 3 1 4 4 4 4 4
## 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
## 4 1 1 4 4 4 1 3 3 4 4 4 4 4 4 4
## 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
## 3 3 3 3 3 3 3 3 3 3 3 2 1 4 3 2
## 680 681 682 684 685 686 687 688 689 690 691 692 693 694 696 697
## 2 2 1 4 1 2 2 3 3 2 2 2 3 3 2 4
## 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713
## 4 2 4 4 4 3 3 3 3 3 1 4 3 4 1 4
## 714 715 716 717 719 720 721 722 723 724 725 726 727 728 731 735
## 1 1 1 1 4 1 1 4 4 4 4 4 3 3 3 1
## 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751
## 3 1 2 3 4 4 1 3 3 3 2 3 1 3 2 2
## 752 753 754 755 757 758 759 760 761 762 763 764 765 766 767 768
## 1 4 3 1 4 1 1 4 4 1 2 1 2 2 1 1
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 1 1 2 1 1 1 3 1 3 4 4 4 4 4 4 4
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 4 1 4 4 1 1 4 4 3 3 3 4 3 2 3 3
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 3 3 4 3 4 2 2 2 2 1 1 1 4 4 4
## 817 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
## 1 4 4 1 4 2 1 1 4 2 1 3 4 4 2 2
## 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849
## 4 3 1 2 1 2 1 1 1 2 3 4 1 1 3 1
## 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 866
## 1 4 1 1 3 2 2 2 3 2 3 2 3 3 3 3
## 867 868 869 871 872 873 874 875 876 877 878 879 880 881 882 883
## 3 3 3 3 3 3 3 4 1 3 1 4 1 1 1 1
## 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
## 4 2 1 4 4 4 1 4 1 1 1 1 1 1 1 1
## 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
## 1 1 1 1 2 1 1 1 1 3 4 1 4 4 3 3
## 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931
## 4 3 2 1 2 1 1 4 1 4 2 2 1 1 1 1
## 932 933 934 935 936 937 938 940 942 943 944 945 946 947 948 949
## 1 2 3 3 3 3 3 2 2 2 1 2 4 4 1 1
## 950 951 952 953 956 957 958 959 960 961 962 963 964 965 966 967
## 3 1 1 1 4 1 2 1 2 1 1 1 1 1 3 3
## 968 969 970 971 972 973 974 976 977 978 979 980 982 983 984 985
## 2 4 4 3 3 3 4 2 1 3 4 4 2 2 2 1
## 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## 4 3 4 1 1 3 1 2 3 1 3 1 4 2 3 4
## 1002 1003 1004 1005 1006 1007 1008 1009 1011 1012 1013 1014 1015 1016 1017 1018
## 3 3 1 3 1 1 1 1 4 4 1 4 1 3 3 3
## 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
## 2 2 2 4 3 4 1 3 3 4 1 1 1 4 4 1
## 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
## 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1064 1065 1066 1067
## 3 2 3 2 2 1 1 1 1 1 1 1 3 4 1 2
## 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083
## 2 1 2 3 2 3 4 3 3 2 2 2 2 1 1 1
## 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099
## 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2
## 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
## 2 2 4 2 1 4 1 1 1 2 3 2 2 2 2 2
## 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## 2 2 1 1 3 3 1 3 2 1 1 1 2 2 3 3
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
## 3 2 2 3 2 3 3 3 3 3 1 2 2 1 1 2
## 1148 1149 1150 1151 1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165
## 2 2 2 2 4 1 2 4 2 4 2 1 1 1 4 4
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 2 3 3 4 4 1 3 2 3 3 4 1 1 3 3 2
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197
## 4 2 2 4 1 1 1 4 1 3 3 1 2 3 3 3
## 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1209 1210 1211 1212 1213 1215
## 1 2 2 2 1 2 4 1 2 4 2 1 2 2 2 1
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
## 1 1 2 2 1 2 4 1 1 2 2 1 1 4 3 3
## 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247
## 3 3 3 3 4 4 2 2 1 2 2 1 4 4 1 1
## 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263
## 2 3 4 2 3 1 3 2 2 3 3 3 3 3 2 1
## 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279
## 2 2 1 1 4 1 2 1 3 3 4 1 2 3 2 2
## 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295
## 1 2 1 4 1 1 1 1 4 4 1 1 2 2 2 2
## 1296 1297 1298 1299 1300 1301 1302 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 4 4 4 2 1 2 2 1 4 4 4 2 1 1 1 2
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 1 1 2 1 4 2 1 2 1 4 1 2 1 4 1 4
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 4 4 1 3 4 3 2 1 3 3 4 2 2 2 2 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 1 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 1 2 2 2 2 2 2 2 4 2 2 3 3 1 4 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 3 3 3 3 1 2 2 3 2 3 2 1 4 4 4 4
## 1393 1394 1395 1396 1397 1398 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
## 4 4 4 3 4 3 2 3 4 3 4 1 1 2 4 1
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425
## 1 1 1 2 2 4 1 1 4 1 1 2 1 4 4 4
## 1426 1427 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 4 1 3 3 3 3 4 3 3 1 1 4 4 4 1 4
## 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458
## 1 1 4 4 4 4 4 1 3 1 2 2 4 4 1 1
## Objective function:
## build swap
## 0.718 0.705
##
## Available components:
## [1] "medoids" "id.med" "clustering" "objective" "isolation"
## [6] "clusinfo" "silinfo" "diss" "call"#Checking length
pamcluster <- clusterpam.papa$clustering
length(pamcluster)## [1] 1376#binding to originaldata
dailyscale.pam <- cbind(dailyscale,pamcluster)
#plotting clustered data points
ggplot(dailyscale.pam,aes(x=lteq,y=posaff)) +
geom_point(alpha=.6, color=factor(pamcluster))
pamauto <- pamk(dist.all,krange=2:10,criterion="asw", usepam=TRUE,
scaling=FALSE, alpha=0.001, diss=TRUE,
critout=FALSE, ns=10, seed=NULL)
pamauto## $pamobject
## Medoids:
## ID
## [1,] "598" "653"
## [2,] "63" "78"
## [3,] "738" "802"
## Clustering vector:
## 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
## 1 1 2 2 3 3 3 2 2 2 2 2 1 2 2 2
## 20 21 22 23 27 28 29 30 31 32 37 38 39 40 41 42
## 1 1 1 2 1 1 1 1 2 2 2 2 2 2 1 2
## 43 44 47 48 49 51 52 53 54 55 56 57 58 59 60 61
## 2 1 2 2 2 2 2 2 2 1 3 1 1 1 1 1
## 62 63 64 66 67 68 70 71 72 73 74 75 76 77 78 79
## 3 2 3 3 1 3 2 2 2 2 2 2 2 1 2 3
## 81 84 85 86 87 88 89 90 91 92 93 95 96 97 98 99
## 2 1 1 1 2 2 2 3 3 3 3 2 2 2 2 3
## 101 102 103 105 106 107 108 110 111 112 113 114 115 116 117 118
## 3 3 2 1 3 3 3 2 3 3 3 3 3 3 3 3
## 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
## 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
## 135 136 137 138 140 141 143 144 145 146 147 149 150 151 152 153
## 2 3 3 2 3 3 3 3 3 3 3 3 3 3 1 3
## 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
## 2 2 2 3 3 2 2 2 2 2 2 2 2 1 2 2
## 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185
## 1 2 3 1 1 1 1 1 1 1 1 2 3 3 1 3
## 186 187 188 189 190 191 192 193 194 196 197 198 199 201 202 203
## 2 3 3 3 1 3 3 1 1 2 2 2 2 3 3 3
## 204 205 206 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 2 3 3 3 2 2 2 2 2 2 1 2 1 1 1
## 221 222 223 224 225 226 228 229 230 231 232 233 234 235 236 237
## 1 3 1 1 3 2 2 2 1 1 2 3 2 2 1 1
## 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253
## 2 1 1 1 3 2 2 3 3 2 3 2 3 1 3 3
## 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
## 1 3 3 3 2 2 2 2 1 2 2 2 2 1 2 1
## 270 271 272 273 274 275 276 277 278 279 280 281 282 283 285 286
## 3 2 2 2 2 2 1 1 1 2 1 1 1 1 1 1
## 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
## 1 1 2 1 1 1 1 1 1 2 2 2 1 1 2 1
## 303 304 305 306 307 308 309 312 313 314 315 316 317 318 319 320
## 3 2 2 2 2 2 1 2 2 2 2 3 3 1 1 2
## 321 323 324 325 326 327 328 329 330 331 332 333 334 335 343 344
## 2 2 2 2 2 2 2 3 2 2 2 2 2 2 1 2
## 345 346 347 348 349 350 352 353 354 355 356 358 359 360 361 364
## 1 2 1 2 2 2 2 2 2 1 1 1 1 2 3 3
## 365 366 367 368 369 370 371 372 373 374 376 377 378 379 380 381
## 3 3 2 2 2 2 3 2 2 3 1 1 1 2 2 1
## 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 1 2 3 2 3 2 2 1 1 3 3 3 1 1 3 3
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 3 3 3 1 1 3 3 1 3 1 1 1 2 1 1 1
## 414 415 416 417 418 419 422 423 424 425 426 427 428 429 430 431
## 1 2 2 2 2 2 1 2 3 3 3 3 3 3 3 2
## 432 433 434 435 436 437 438 439 441 442 443 444 445 446 447 448
## 2 2 2 2 3 1 1 3 2 2 3 1 3 3 2 2
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 2 2 2 1 1 1 1 3 1 1 1 2 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 1 1 2 2 2 1 2 2 3 3 2 1 1 1 1 1
## 481 483 485 486 487 488 489 490 491 492 493 494 495 496 497 498
## 2 1 2 2 2 1 1 1 1 1 1 2 1 2 1 1
## 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514
## 1 1 2 3 1 1 1 1 1 2 2 2 2 2 2 2
## 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530
## 1 1 3 3 2 2 3 2 3 3 1 1 1 2 3 3
## 531 533 534 535 536 537 538 539 540 541 542 543 544 545 546 548
## 3 1 3 3 3 1 1 1 1 1 1 1 2 3 2 3
## 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## 3 3 3 2 3 3 3 3 1 3 3 2 3 1 1 2
## 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
## 3 1 1 2 2 2 2 2 2 2 2 1 3 3 3 3
## 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596
## 1 1 1 1 2 2 1 1 2 1 1 2 1 1 1 2
## 597 598 599 601 602 603 604 605 606 607 609 610 611 612 613 614
## 1 1 1 2 1 1 2 1 1 1 2 2 2 2 1 1
## 615 616 617 618 619 620 621 622 623 624 625 626 628 629 630 631
## 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2
## 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
## 1 1 1 1 1 2 1 1 2 3 2 1 1 1 1 1
## 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
## 1 2 1 1 1 1 3 3 3 1 1 1 1 1 1 1
## 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679
## 3 3 3 3 3 3 3 3 3 3 3 2 2 1 3 2
## 680 681 682 684 685 686 687 688 689 690 691 692 693 694 696 697
## 2 2 2 1 1 2 2 3 3 2 2 2 3 3 2 1
## 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713
## 1 2 1 1 1 3 3 3 3 3 1 1 3 1 1 1
## 714 715 716 717 719 720 721 722 723 724 725 726 727 728 731 735
## 2 1 1 1 1 1 3 1 1 1 1 1 3 3 3 2
## 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751
## 3 2 3 3 1 1 3 3 3 3 2 3 1 3 2 2
## 752 753 754 755 757 758 759 760 761 762 763 764 765 766 767 768
## 1 1 3 2 1 2 1 1 1 2 2 1 2 2 2 2
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 2 1 2 2 1 1 3 1 3 1 1 1 1 1 1 1
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 1 1 1 1 2 2 1 1 3 3 3 1 3 2 3 3
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 3 3 1 3 1 2 2 2 2 2 2 2 1 1 1
## 817 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
## 2 1 1 1 1 2 2 2 1 2 1 3 1 1 2 2
## 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849
## 1 3 1 3 2 2 1 2 2 2 3 1 1 1 3 2
## 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 866
## 2 1 2 1 3 2 2 3 3 2 3 2 3 3 3 3
## 867 868 869 871 872 873 874 875 876 877 878 879 880 881 882 883
## 3 3 3 3 3 3 3 1 1 3 1 1 2 1 2 1
## 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
## 1 2 2 1 1 1 2 1 2 2 2 3 2 2 1 2
## 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915
## 2 2 2 2 2 1 1 1 2 3 1 3 1 1 3 3
## 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931
## 1 3 2 3 3 3 1 1 2 1 2 2 1 2 2 2
## 932 933 934 935 936 937 938 940 942 943 944 945 946 947 948 949
## 1 2 3 3 3 3 3 2 2 2 2 2 1 1 1 2
## 950 951 952 953 956 957 958 959 960 961 962 963 964 965 966 967
## 3 3 2 1 1 1 2 2 2 1 1 1 1 2 3 3
## 968 969 970 971 972 973 974 976 977 978 979 980 982 983 984 985
## 2 1 1 3 3 3 1 2 2 3 1 1 2 2 2 1
## 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001
## 1 3 1 1 3 3 2 2 3 3 3 1 1 3 3 1
## 1002 1003 1004 1005 1006 1007 1008 1009 1011 1012 1013 1014 1015 1016 1017 1018
## 3 3 3 3 1 2 2 2 1 1 2 1 3 3 3 3
## 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034
## 2 2 2 1 3 1 3 3 3 1 2 1 1 1 1 1
## 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
## 1 1 1 2 2 2 2 2 2 2 2 3 2 2 2 2
## 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1064 1065 1066 1067
## 3 2 3 2 2 2 2 1 1 1 1 3 3 1 3 3
## 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083
## 2 3 2 3 2 3 1 3 3 3 2 2 2 1 2 1
## 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
## 2 2 1 2 1 1 2 1 2 2 3 2 3 2 2 2
## 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
## 2 2 2 3 3 3 1 3 2 1 2 2 3 2 3 3
## 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
## 3 2 2 3 2 3 3 3 3 3 2 2 2 3 2 2
## 1148 1149 1150 1151 1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165
## 2 2 2 2 1 2 2 1 2 1 2 2 2 1 1 1
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 2 3 3 1 1 1 3 2 3 3 1 2 1 3 3 3
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197
## 1 2 2 1 2 3 3 1 1 3 3 1 3 3 3 3
## 1198 1199 1200 1201 1202 1203 1204 1205 1207 1208 1209 1210 1211 1212 1213 1215
## 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231
## 2 1 2 2 2 2 1 2 1 2 2 1 2 1 3 3
## 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247
## 3 3 3 3 1 1 2 2 1 2 2 2 1 1 1 2
## 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263
## 2 3 1 2 3 2 3 3 2 3 3 3 3 3 2 2
## 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279
## 2 2 3 2 1 2 2 3 3 3 1 2 3 3 2 2
## 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295
## 2 2 1 1 1 1 2 1 1 1 2 2 2 2 2 2
## 1296 1297 1298 1299 1300 1301 1302 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 2
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 2 1 2 2 1 2 2 2 2 1 2 2 2 1 2 1
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 1 1 1 3 1 3 2 3 3 3 3 2 2 2 2 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 2 2 2 2 2 2 2 2 1 2 2 3 3 1 1 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 3 3 3 3 1 2 2 3 3 3 3 1 1 1 1 1
## 1393 1394 1395 1396 1397 1398 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
## 1 1 1 3 1 3 2 3 1 3 1 1 2 2 1 2
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425
## 3 2 1 2 2 1 1 1 1 2 1 2 1 1 1 1
## 1426 1427 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 1 2 3 3 3 3 1 3 3 2 1 1 1 1 1 1
## 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458
## 2 1 1 1 1 1 1 1 3 1 2 2 1 1 2 2
## Objective function:
## build swap
## 0.850 0.787
##
## Available components:
## [1] "medoids" "id.med" "clustering" "objective" "isolation"
## [6] "clusinfo" "silinfo" "diss" "call"
##
## $nc
## [1] 3
##
## $crit
## [1] 0.000 0.335 0.381 0.317 0.326 0.336 0.349 0.335 0.334 0.333#Obtain medoids
pamauto$pamobject$id.med## [1] 598 63 738#binding new cluster assignment to originaldata
dailyscale.pam$pamnew <- pamauto$pamobject$clustering
#plotting clustered data points with the medoids
ggplot(dailyscale.pam,aes(x=lteq,y=posaff)) +
geom_point(alpha=.6, color=factor(dailyscale.pam$pamnew)) +
geom_point(data=dailyscale.pam[598,],aes(x=lteq,y=posaff),color=2,size=5,shape=18) +
geom_point(data=dailyscale.pam[63,],aes(x=lteq,y=posaff),color=1,size=5,shape=18) +
geom_point(data=dailyscale.pam[738,],aes(x=lteq,y=posaff),color=4,size=5,shape=18)
Example Big Five
The following chunk is just to demonstrate the data wrangling.
require(tidyverse)
dd <- read.csv2('http://e-scientifics.de/content/datasets/Big5_GEMI_R_recoded.csv') # read data, items already recoded
dd <- cbind(1:nrow(dd), dd)
colnames(dd)[1] <- "subj"
getwd()
readr::write_csv(dd, "big5_gemi.csv")
# Neuroticism
dd <- dplyr::rowwise(dd) %>% dplyr::mutate(neo_n = mean(c(neo_ffi_1_rec, neo_ffi_6, neo_ffi_11, neo_ffi_16_rec, neo_ffi_21, neo_ffi_26, neo_ffi_31_rec, neo_ffi_36, neo_ffi_41, neo_ffi_46_rec, neo_ffi_51, neo_ffi_56)))
# Extraversion
dd <- dplyr::rowwise(dd) %>% dplyr::mutate(neo_e = mean(c(neo_ffi_2, neo_ffi_7, neo_ffi_12_rec, neo_ffi_17, neo_ffi_22, neo_ffi_27_rec, neo_ffi_32, neo_ffi_37, neo_ffi_42_rec, neo_ffi_47, neo_ffi_52, neo_ffi_57_rec)))
# Openness to experience
dd <- dplyr::rowwise(dd) %>% dplyr::mutate(neo_o = mean(c(neo_ffi_3_rec, neo_ffi_8_rec, neo_ffi_13, neo_ffi_18_rec, neo_ffi_23_rec, neo_ffi_28, neo_ffi_33_rec, neo_ffi_38_rec, neo_ffi_43, neo_ffi_48_rec, neo_ffi_53, neo_ffi_58)))
# Agreeableness
dd <- dplyr::rowwise(dd) %>% dplyr::mutate(neo_a = mean(c(neo_ffi_4, neo_ffi_9_rec, neo_ffi_14_rec, neo_ffi_19, neo_ffi_24_rec, neo_ffi_29_rec, neo_ffi_34, neo_ffi_39_rec, neo_ffi_44_rec, neo_ffi_49, neo_ffi_54_rec, neo_ffi_59_rec)))
# Conscientiousness
dd <- dplyr::rowwise(dd) %>% dplyr::mutate(neo_c = mean(c(neo_ffi_5, neo_ffi_10, neo_ffi_15_rec, neo_ffi_20, neo_ffi_25, neo_ffi_30_rec, neo_ffi_35, neo_ffi_40, neo_ffi_45_rec, neo_ffi_50, neo_ffi_55_rec, neo_ffi_60)))
readr::write_csv(dd, "big5_gemi_scores.csv")And now some clustering …
require(tidyverse)
dd <- readr::read_csv("http://md.psych.bio.uni-goettingen.de/mv/data/div/big5_gemi_scores.csv")## Rows: 160 Columns: 68
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (68): subj, vpage, vpsex, neo_ffi_1_rec, neo_ffi_2, neo_ffi_3_rec, neo_f...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# some descriptives
dd %>% dplyr::select(subj:vpsex, neo_n:neo_c) %>% psych::describe()## vars n mean sd median trimmed mad min max range skew
## subj 1 160 80.50 46.33 80.50 80.50 59.30 1.00 160.00 159.00 0.00
## vpage 2 160 22.98 4.09 22.00 22.24 1.48 18.00 46.00 28.00 2.95
## vpsex 3 160 0.50 0.50 0.50 0.50 0.74 0.00 1.00 1.00 0.00
## neo_n 4 160 -0.28 0.70 -0.33 -0.30 0.74 -1.83 1.75 3.58 0.28
## neo_e 5 160 0.49 0.48 0.50 0.49 0.37 -1.08 1.58 2.67 -0.18
## neo_o 6 160 0.68 0.54 0.75 0.71 0.56 -0.83 1.83 2.67 -0.39
## neo_a 7 160 0.62 0.49 0.67 0.63 0.49 -0.58 1.83 2.42 -0.16
## neo_c 8 160 0.65 0.61 0.75 0.67 0.62 -1.08 1.92 3.00 -0.33
## kurtosis se
## subj -1.22 3.66
## vpage 11.57 0.32
## vpsex -2.01 0.04
## neo_n -0.31 0.06
## neo_e 0.28 0.04
## neo_o -0.31 0.04
## neo_a -0.29 0.04
## neo_c -0.32 0.05dd %>% dplyr::select(subj:vpsex, neo_n:neo_c) %>% psych::describeBy(dd$vpsex)##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew
## subj 1 80 80.10 47.15 78.50 80.27 59.30 1.00 160.00 159.00 -0.02
## vpage 2 80 22.69 4.54 21.00 21.88 1.48 18.00 46.00 28.00 3.32
## vpsex 3 80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NaN
## neo_n 4 80 -0.17 0.68 -0.17 -0.19 0.68 -1.50 1.33 2.83 0.22
## neo_e 5 80 0.52 0.48 0.58 0.52 0.37 -0.92 1.58 2.50 -0.22
## neo_o 6 80 0.70 0.54 0.75 0.73 0.62 -0.67 1.83 2.50 -0.31
## neo_a 7 80 0.82 0.47 0.83 0.84 0.49 -0.25 1.83 2.08 -0.34
## neo_c 8 80 0.77 0.56 0.83 0.79 0.49 -0.50 1.92 2.42 -0.36
## kurtosis se
## subj -1.22 5.27
## vpage 13.48 0.51
## vpsex NaN 0.00
## neo_n -0.61 0.08
## neo_e 0.29 0.05
## neo_o -0.41 0.06
## neo_a -0.26 0.05
## neo_c -0.41 0.06
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew
## subj 1 80 80.90 45.80 83.50 80.67 60.05 2.00 159.00 157.00 0.03
## vpage 2 80 23.26 3.61 22.00 22.61 1.48 19.00 39.00 20.00 2.18
## vpsex 3 80 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN
## neo_n 4 80 -0.39 0.71 -0.42 -0.42 0.68 -1.83 1.75 3.58 0.38
## neo_e 5 80 0.46 0.48 0.50 0.45 0.49 -1.08 1.58 2.67 -0.14
## neo_o 6 80 0.66 0.53 0.75 0.69 0.49 -0.83 1.67 2.50 -0.46
## neo_a 7 80 0.41 0.42 0.42 0.43 0.37 -0.58 1.25 1.83 -0.33
## neo_c 8 80 0.53 0.64 0.54 0.54 0.56 -1.08 1.83 2.92 -0.20
## kurtosis se
## subj -1.28 5.12
## vpage 5.50 0.40
## vpsex NaN 0.00
## neo_n -0.03 0.08
## neo_e 0.22 0.05
## neo_o -0.29 0.06
## neo_a -0.32 0.05
## neo_c -0.39 0.07# rescaling of the cluster variables...
dd.t <- dd %>% dplyr::select(neo_n:neo_c) %>% scale() %>% data.frame
colnames(dd.t) <- c("neo_n_z","neo_e_z", "neo_o_z", "neo_a_z", "neo_c_z")
dd <- cbind(dd, dd.t)
# the distances
dd.s <- dd %>% dplyr::filter(vpsex == 1, vpage > 22) %>% dplyr::select(neo_n_z:neo_c_z)
dists <- dd.s %>% dist()
dists[1:6]## [1] 2.53 4.10 3.23 1.70 2.13 2.90#cutree(hclust(dists,method="single"),h=3.8)
# some linkage variants as proposed by Everitt
plot(hclust(dists, method="single"), ylab="Height", sub="Single linkage")
plot(hclust(dists, method="complete"),ylab="Height", sub="Complete linkage")
plot(hclust(dists, method="average"), ylab="Height", sub="Average linkage")
# k-means
#there are random starts involved so we set a seed
set.seed(1234)
#running a cluster analysis
# we set 3 Clusters and use the scores
model <- dd %>% dplyr::select(neo_n_z:neo_c_z) %>% kmeans(centers=3, iter.max=1000, nstart=1000)
model## K-means clustering with 3 clusters of sizes 47, 62, 51
##
## Cluster means:
## neo_n_z neo_e_z neo_o_z neo_a_z neo_c_z
## 1 -0.717 0.604 0.588 0.580 0.355
## 2 0.647 -0.550 0.467 -0.609 -0.491
## 3 -0.126 0.112 -1.110 0.206 0.270
##
## Clustering vector:
## [1] 1 1 2 1 1 3 2 1 2 2 1 2 1 1 2 1 1 2 3 3 3 2 3 1 3 1 2 3 3 1 3 3 3 2 2 1 1
## [38] 2 3 1 3 2 2 2 2 3 3 3 2 2 2 1 2 3 2 3 1 2 3 3 2 3 2 3 2 2 3 3 3 1 2 2 2 2
## [75] 2 1 1 2 1 2 2 2 3 2 3 2 2 1 2 3 2 1 3 1 3 3 2 1 3 1 3 3 3 3 1 1 2 1 3 1 1
## [112] 1 3 2 2 2 1 3 1 1 1 1 2 2 2 3 2 1 2 1 2 2 3 2 1 2 1 1 3 2 2 1 3 3 3 1 3 2
## [149] 2 3 2 2 3 2 3 1 3 2 1 3
##
## Within cluster sum of squares by cluster:
## [1] 145 248 156
## (between_SS / total_SS = 30.9 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# if we want to use the clusters furtheron f. e. for some analyses, we store the cluster assignment
dd$cluster <- model$cluster
# we visualize the clusters
# we store the above calculated unstandardized means
m_z <- dd %>% dplyr::group_by(cluster) %>% dplyr::select(neo_n_z:neo_c_z) %>% dplyr::summarize_all(mean)## Adding missing grouping variables: `cluster`m_u <- dd %>% dplyr::group_by(cluster) %>% dplyr::select(neo_n:neo_c) %>% dplyr::summarize_all(mean)## Adding missing grouping variables: `cluster`dd %>% ggplot(aes(x=neo_n,y=neo_e)) +
geom_point(color=model$cluster, alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"neo_n"]),y=as.numeric(m_u[1,"neo_e"])),color=1,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"neo_n"]),y=as.numeric(m_u[2,"neo_e"])),color=2,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"neo_n"]),y=as.numeric(m_u[3,"neo_e"])),color=3,size=5,shape=18)
dd %>% ggplot(aes(x=neo_e,y=neo_o)) +
geom_point(color=model$cluster, alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"neo_e"]),y=as.numeric(m_u[1,"neo_o"])),color=1,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"neo_e"]),y=as.numeric(m_u[2,"neo_o"])),color=2,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"neo_e"]),y=as.numeric(m_u[3,"neo_o"])),color=3,size=5,shape=18)
dd %>% ggplot(aes(x=neo_o,y=neo_a)) +
geom_point(color=model$cluster, alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"neo_o"]),y=as.numeric(m_u[1,"neo_a"])),color=1,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"neo_o"]),y=as.numeric(m_u[2,"neo_a"])),color=2,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"neo_o"]),y=as.numeric(m_u[3,"neo_a"])),color=3,size=5,shape=18)
dd %>% ggplot(aes(x=neo_a,y=neo_c)) +
geom_point(color=model$cluster, alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"neo_a"]),y=as.numeric(m_u[1,"neo_c"])),color=1,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"neo_a"]),y=as.numeric(m_u[2,"neo_c"])),color=2,size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"neo_a"]),y=as.numeric(m_u[3,"neo_c"])),color=3,size=5,shape=18)
# we can also use mclust::clPairs() to get an grafical overview
dd %>% dplyr::select(neo_n:neo_c) %>% mclust::clPairs(dd$cluster)
# some graph to choose a suitable number of clusters
#making a empty dataframe
criteria <- data.frame()
#setting range of k
nk <- 1:10
#loop for range of clusters
for (k in nk) {
# model <- kmeans(dailyscale[,c("lteq","posaff")], k)
model <- dd %>% dplyr::select(neo_n:neo_c) %>% kmeans(centers=k, iter.max=1000, nstart=1000)
criteria <- rbind(criteria,c(k,model$tot.withinss,model$betweenss,model$totss))
}
#renaming columns
names(criteria) <- c("k","tot.withinss","betweenss","totalss")
#scree plot
ggplot(criteria, aes(x=k)) +
geom_point(aes(y=tot.withinss),color="red") +
geom_line(aes(y=tot.withinss),color="red") +
geom_point(aes(y=betweenss),color="blue") +
geom_line(aes(y=betweenss),color="blue") +
xlab("k = number of clusters") + ylab("Sum of Squares (within = red, between = blue)")
## Model Based Clustering
# source
# https://cran.r-project.org/web/packages/mclust/vignettes/mclust.html
library(mclust)
X <- dd %>% dplyr::select(neo_n_z:neo_c_z)
head(X)## neo_n_z neo_e_z neo_o_z neo_a_z neo_c_z
## 1 0.162 0.714 -0.182 0.613 0.437
## 2 -0.549 0.369 0.906 -1.090 0.847
## 3 0.517 -0.149 0.440 -1.601 0.573
## 4 -1.378 0.369 0.440 1.294 2.080
## 5 -0.549 0.196 1.061 1.635 0.984
## 6 0.162 1.231 -0.803 0.613 0.573BIC <- mclust::mclustBIC(X)
plot(BIC)
summary(BIC)## Best BIC values:
## EII,1 VII,1 EII,2
## BIC -2296 -2296 -2299.02
## BIC diff 0 0 -3.29mod1 <- mclust::Mclust(X, x = BIC)
# summary(mod1, parameters = TRUE)
# `mclustBIC()` recommends 1 cluster, so the plot is not very informative ;-)
plot(mod1, what = "classification")
Example Medical Costs
Columns
age: age of primary beneficiary
sex: insurance contractor gender, female, male
bmi: Body mass index, providing an understanding of body, weights that are relatively high or low relative to height, objective index of body weight (kg / m ^ 2) using the ratio of height to weight, ideally 18.5 to 24.9
children: Number of children covered by health insurance / Number of dependents
smoker: Smoking
region: the beneficiary’s residential area in the US, northeast, southeast, southwest, northwest.
charges: Individual medical costs billed by health insurance
Download from github
require(tidyverse)
set.seed(1234)
# the data come from https://www.kaggle.com/mirichoi0218/insurance
# alternatively: https://github.com/stedy/Machine-Learning-with-R-datasets
# we read from a local server for conveniance
dd <- readr::read_csv("http://md.psych.bio.uni-goettingen.de/mv/data/div/insurance.csv")## Rows: 1338 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): sex, smoker, region
## dbl (4): age, bmi, children, charges
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.dd <- cbind(1:nrow(dd), dd)
names(dd)[1] <- "subj"
dd <- dd %>% dplyr::mutate(gender_f = ifelse(sex == "female", 1, 0)) %>% dplyr::mutate(smoker_t = ifelse(smoker == "yes", 1, 0))
# rescaling of the cluster variables...
dd.t <- dd %>% dplyr::select(age, gender_f, bmi, children, smoker_t, charges) %>% scale() %>% data.frame()
colnames(dd.t) <- c("age_z","gender_f_z", "bmi_z", "children_z", "smoker_t_z", "charges_z")
dd <- cbind(dd, dd.t)
# we add a categorial variable bmi_class
dd <- dd %>% dplyr::mutate(bmi_class = ifelse(bmi <= 18.5, 0,
ifelse(bmi >18.5 & bmi <= 25, 1,
ifelse(bmi > 25 & bmi < 30, 2, 3))))
# we take a look at the data structure
head(dd)## subj age sex bmi children smoker region charges gender_f smoker_t
## 1 1 19 female 27.9 0 yes southwest 16885 1 1
## 2 2 18 male 33.8 1 no southeast 1726 0 0
## 3 3 28 male 33.0 3 no southeast 4449 0 0
## 4 4 33 male 22.7 0 no northwest 21984 0 0
## 5 5 32 male 28.9 0 no northwest 3867 0 0
## 6 6 31 female 25.7 0 no southeast 3757 1 0
## age_z gender_f_z bmi_z children_z smoker_t_z charges_z bmi_class
## 1 -1.438 1.010 -0.453 -0.9083 1.970 0.298 2
## 2 -1.509 -0.989 0.509 -0.0787 -0.507 -0.953 3
## 3 -0.798 -0.989 0.383 1.5803 -0.507 -0.728 3
## 4 -0.442 -0.989 -1.305 -0.9083 -0.507 0.720 1
## 5 -0.513 -0.989 -0.292 -0.9083 -0.507 -0.777 2
## 6 -0.584 1.010 -0.807 -0.9083 -0.507 -0.786 2# todo: descriptive plot
# the distances
# we reduce our observations
s.sel <- sample(dd$subj, 50)
dd.s <- dd[dd$subj %in% s.sel,]
dists <- dd.s %>% dplyr::select(age_z,gender_f_z, bmi_z, children_z, smoker_t_z, charges_z) %>% dist()
dists[1:6]## [1] 3.87 3.15 2.93 2.90 2.84 2.53# dists
# some linkage variants as proposed by Everitt
plot(hclust(dists, method="single"), ylab="Height", sub="Single linkage")
plot(hclust(dists, method="complete"),ylab="Height", sub="Complete linkage")
plot(hclust(dists, method="average"), ylab="Height", sub="Average linkage")
# we create an elbow visualization, a graph to choose a suitable number of clusters
# making an empty dataframe
criteria <- data.frame()
#setting range of k
nk <- 1:10
#loop for range of clusters
for (k in nk) {
#model <- dd %>% dplyr::select(age, sex.f, bmi, children, smoker.t, charges) %>% kmeans(centers=k, iter.max=1000, nstart=1000)
model <- dd %>% dplyr::select(age_z,gender_f_z, bmi_z, children_z, smoker_t_z, charges_z) %>% kmeans(centers=k, iter.max=1000, nstart=1000)
criteria <- rbind(criteria,c(k,model$tot.withinss,model$betweenss,model$totss))
}
#renaming columns
names(criteria) <- c("k","tot.withinss","betweenss","totalss")
#scree plot
ggplot(criteria, aes(x=k)) +
geom_point(aes(y=tot.withinss),color="red") +
geom_line(aes(y=tot.withinss),color="red") +
geom_point(aes(y=betweenss),color="blue") +
geom_line(aes(y=betweenss),color="blue") +
xlab("k = number of clusters") + ylab("Sum of Squares (within = red, between = blue)")
# due to our visual impression, 5 (3, 4, 5) clusters might be a good selection
# k-means
#running a cluster analysis
# we set 3 Clusters and use the scores
n_clusters = 5
model <- dd %>% dplyr::select(age_z, gender_f_z, bmi_z, children_z, smoker_t_z, charges_z) %>% kmeans(centers=n_clusters, iter.max=1000, nstart=1000)
# model
attributes(model)## $names
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"
##
## $class
## [1] "kmeans"# if we want to use the clusters furtheron f. e. for some analyses, we store the cluster assignment
dd$kmc_5 <- factor(model$cluster)
# we store the above calculated unstandardized means
m_u <- dd %>% dplyr::group_by(kmc_5) %>% dplyr::select(age, gender_f, bmi, children, smoker_t, charges) %>% dplyr::summarize_all(mean)## Adding missing grouping variables: `kmc_5`# we visualize the clusters to check the effect of the clustering variables
library(scales)##
## Attache Paket: 'scales'
##
## Die folgenden Objekte sind maskiert von 'package:psych':
##
## alpha, rescale
##
## Das folgende Objekt ist maskiert 'package:purrr':
##
## discard
##
## Das folgende Objekt ist maskiert 'package:readr':
##
## col_factor# hue_pal()(n_clusters)
# show_col(hue_pal()(n_clusters))
dd %>% ggplot(aes(x=age,y=charges, color=kmc_5)) +
geom_point(alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"age"]),y=as.numeric(m_u[1,"charges"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"age"]),y=as.numeric(m_u[2,"charges"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"age"]),y=as.numeric(m_u[3,"charges"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"age"]),y=as.numeric(m_u[4,"charges"])),color=hue_pal()(n_clusters)[4],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[5,"age"]),y=as.numeric(m_u[5,"charges"])),color=hue_pal()(n_clusters)[5],size=5,shape=18)
dd %>% ggplot(aes(x=bmi,y=charges, color=kmc_5)) +
geom_point(alpha=.6) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"bmi"]),y=as.numeric(m_u[1,"charges"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"bmi"]),y=as.numeric(m_u[2,"charges"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"bmi"]),y=as.numeric(m_u[3,"charges"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"bmi"]),y=as.numeric(m_u[4,"charges"])),color=hue_pal()(n_clusters)[4],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[5,"bmi"]),y=as.numeric(m_u[5,"charges"])),color=hue_pal()(n_clusters)[5],size=5,shape=18)
dd %>% ggplot(aes(x=children,y=charges, color=kmc_5)) +
# geom_point(alpha=.6) +#plotting alll the points
geom_jitter(alpha=.6, width=0.2) +#plotting alll the points
#plotting the centroids
geom_point(aes(x=as.numeric(m_u[1,"children"]),y=as.numeric(m_u[1,"charges"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"children"]),y=as.numeric(m_u[2,"charges"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"children"]),y=as.numeric(m_u[3,"charges"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"children"]),y=as.numeric(m_u[4,"charges"])),color=hue_pal()(n_clusters)[4],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[5,"children"]),y=as.numeric(m_u[5,"charges"])),color=hue_pal()(n_clusters)[5],size=5,shape=18)
# we check other variables in the cluster Space
## Model Based Clustering
# source
# https://cran.r-project.org/web/packages/mclust/vignettes/mclust.html
library(mclust)
# X <- dd %>% dplyr::select(age, sex.f, bmi, children, smoker.t, charges)
X <- dd %>% dplyr::select(age_z:charges_z)
head(X)## age_z gender_f_z bmi_z children_z smoker_t_z charges_z
## 1 -1.438 1.010 -0.453 -0.9083 1.970 0.298
## 2 -1.509 -0.989 0.509 -0.0787 -0.507 -0.953
## 3 -0.798 -0.989 0.383 1.5803 -0.507 -0.728
## 4 -0.442 -0.989 -1.305 -0.9083 -0.507 0.720
## 5 -0.513 -0.989 -0.292 -0.9083 -0.507 -0.777
## 6 -0.584 1.010 -0.807 -0.9083 -0.507 -0.786BIC <- mclust::mclustBIC(X)
plot(BIC)
summary(BIC)## Best BIC values:
## VII,9 VII,8 VII,7
## BIC -19171 -19329 -19624
## BIC diff 0 -158 -453mod1 <- mclust::Mclust(X, x = BIC)
# this output is long, just to show that it exists
# summary(mod1, parameters = TRUE)
plot(mod1, what = "BIC")
plot(mod1, what = "classification")
# we store the model based classification
dd$mbc_9 <- mod1$classification
# we might want to inspect the cluster means in original scale
(m_u <- dd %>% dplyr::group_by(mbc_9) %>% dplyr::select(age, gender_f, bmi, children, smoker_t, charges) %>% dplyr::summarize_all(mean) )## Adding missing grouping variables: `mbc_9`## # A tibble: 9 × 7
## mbc_9 age gender_f bmi children smoker_t charges
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 36.2 0.507 25.5 1.01 0.978 21892.
## 2 2 24.5 0 28.4 0.324 0 2844.
## 3 3 37.5 0 28.6 2.62 0 8626.
## 4 4 42.2 0.524 39.5 1.02 0 10264.
## 5 5 26.2 1 28.0 0.316 0 4105.
## 6 6 52.6 1 28.7 0.371 0 11651.
## 7 7 40.2 1 29.2 2.58 0 9648.
## 8 8 40.6 0.331 35.7 1.19 1 41938.
## 9 9 53.5 0 29.6 0.396 0 11392.# ... our attention might be drawn to the two clusters that share the highest charges and smokers
# we can look at classification dependent tables
table(dd$gender_f, mod1$classification)##
## 1 2 3 4 5 6 7 8 9
## 0 68 142 143 91 0 0 0 93 139
## 1 70 0 0 100 155 140 151 46 0# or
table(dd$gender_f, dd$mbc_9)##
## 1 2 3 4 5 6 7 8 9
## 0 68 142 143 91 0 0 0 93 139
## 1 70 0 0 100 155 140 151 46 0# we can also use mclust::clPairs() to plot other classifications
table(dd$kmc_5)##
## 1 2 3 4 5
## 237 265 280 273 283mclust::clPairs(X, dd$kmc_5)
table(dd$bmi_class)##
## 0 1 2 3
## 21 226 384 707mclust::clPairs(X, dd$bmi_class)
Example Mall Customers
You are owing a supermarket mall and through membership cards , you have some basic data about your customers like Customer ID, age, gender, annual income and spending score.
Spending Score is something you assign to the customer based on your defined parameters like customer behavior and purchasing data.
These are simulated data for learning purposes.
require(tidyverse)
library(scales)
# the data come from https://www.kaggle.com/mirichoi0218/insurance
# we read from a local server for conveniance
dd <- readr::read_csv("http://md.psych.bio.uni-goettingen.de/mv/data/div/mall_customers.csv")## Rows: 200 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Gender
## dbl (4): CustomerID, Age, Annual Income (k$), Spending Score (1-100)
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# we take a look at the data structure
colnames(dd) <- c("subj", "gender", "age", "income", "spending_score")
head(dd)## # A tibble: 6 × 5
## subj gender age income spending_score
## <dbl> <chr> <dbl> <dbl> <dbl>
## 1 1 Male 19 15 39
## 2 2 Male 21 15 81
## 3 3 Female 20 16 6
## 4 4 Female 23 16 77
## 5 5 Female 31 17 40
## 6 6 Female 22 17 76dd <- dd %>% dplyr::mutate(genderf = ifelse(gender == "Female", 1, 0))
# standardization
dd.z <- dd %>% dplyr::select(age, income, spending_score, genderf) %>% scale() %>% data.frame
colnames(dd.z) <- c("age_z", "income_z", "spending_score_z", "genderf_z")
dd <- cbind(dd, dd.z)
head(dd)## subj gender age income spending_score genderf age_z income_z
## 1 1 Male 19 15 39 0 -1.421 -1.73
## 2 2 Male 21 15 81 0 -1.278 -1.73
## 3 3 Female 20 16 6 1 -1.349 -1.70
## 4 4 Female 23 16 77 1 -1.135 -1.70
## 5 5 Female 31 17 40 1 -0.562 -1.66
## 6 6 Female 22 17 76 1 -1.206 -1.66
## spending_score_z genderf_z
## 1 -0.434 -1.125
## 2 1.193 -1.125
## 3 -1.712 0.884
## 4 1.038 0.884
## 5 -0.395 0.884
## 6 0.999 0.884# we create an elbow visualization, a graph to choose a suitable number of clusters
criteria <- data.frame()
nk <- 1:10
#loop for range of clusters
for (k in nk) {
model <- dd %>% dplyr::select(age_z:genderf_z) %>% kmeans(centers=k, iter.max=1000, nstart=1000)
criteria <- rbind(criteria,c(k,model$tot.withinss,model$betweenss,model$totss))
}
#renaming columns
names(criteria) <- c("k","tot.withinss","betweenss","totalss")
#scree plot
ggplot(criteria, aes(x=k)) +
geom_point(aes(y=tot.withinss),color="red") +
geom_line(aes(y=tot.withinss),color="red") +
geom_point(aes(y=betweenss),color="blue") +
geom_line(aes(y=betweenss),color="blue") +
xlab("k = number of clusters") + ylab("Sum of Squares (within = red, between = blue)")
# k-means 4 Clusters and use the scores
n_clusters = 4
model <- dd %>% dplyr::select(age_z:genderf_z) %>% kmeans(centers=n_clusters, iter.max=1000, nstart=1000)
model## K-means clustering with 4 clusters of sizes 48, 57, 55, 40
##
## Cluster means:
## age_z income_z spending_score_z genderf_z
## 1 0.758 0.0707 -0.813 -1.125
## 2 -0.745 -0.0340 0.677 0.884
## 3 0.663 -0.0663 -0.597 0.884
## 4 -0.759 0.0548 0.832 -1.125
##
## Clustering vector:
## [1] 4 4 3 2 2 2 3 2 1 2 1 2 3 2 1 4 3 4 1 2 1 4 3 4 3 4 3 4 3 2 1 2 1 4 3 2 3
## [38] 2 3 2 3 4 1 2 3 2 3 2 2 2 3 4 2 1 3 1 3 1 2 1 1 4 3 3 1 4 3 3 4 2 1 3 3 3
## [75] 1 4 3 1 2 3 1 4 1 3 2 1 3 2 2 3 3 4 1 3 2 4 3 2 1 4 2 3 1 4 1 2 3 1 1 1 1
## [112] 2 3 4 2 2 3 3 3 3 4 3 2 4 2 2 1 4 1 4 1 4 2 2 1 2 3 4 1 2 3 4 2 2 1 4 1 2
## [149] 3 4 1 4 3 2 3 2 1 2 1 2 3 2 1 2 1 2 1 2 3 4 1 4 1 4 3 2 1 4 1 4 3 2 1 2 3
## [186] 4 3 4 3 2 3 2 1 2 3 2 3 4 1 4
##
## Within cluster sum of squares by cluster:
## [1] 115.1 94.9 100.7 74.0
## (between_SS / total_SS = 51.7 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# if we want to use the clusters furtheron f. e. for some analyses, we store the cluster assignment
dd$kmc_4 <- factor(model$cluster)
# we store the unstandardized means of the cluster variables and take a look at it
( m_u <- dd %>% dplyr::group_by(kmc_4) %>% dplyr::select(age, income, spending_score, genderf) %>% dplyr::summarize_all(mean) )## Adding missing grouping variables: `kmc_4`## # A tibble: 4 × 5
## kmc_4 age income spending_score genderf
## <fct> <dbl> <dbl> <dbl> <dbl>
## 1 1 49.4 62.4 29.2 0
## 2 2 28.4 59.7 67.7 1
## 3 3 48.1 58.8 34.8 1
## 4 4 28.2 62 71.7 0dd %>% ggplot(aes(x=age,y=spending_score, color=kmc_4)) +
geom_point(alpha=.6) +#plotting alll the points
geom_point(aes(x=as.numeric(m_u[1,"age"]),y=as.numeric(m_u[1,"spending_score"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"age"]),y=as.numeric(m_u[2,"spending_score"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"age"]),y=as.numeric(m_u[3,"spending_score"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"age"]),y=as.numeric(m_u[4,"spending_score"])),color=hue_pal()(n_clusters)[4],size=5,shape=18)
dd %>% ggplot(aes(x=income,y=spending_score, color=kmc_4)) +
geom_point(alpha=.6) +#plotting alll the points
geom_point(aes(x=as.numeric(m_u[1,"income"]),y=as.numeric(m_u[1,"spending_score"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"income"]),y=as.numeric(m_u[2,"spending_score"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"income"]),y=as.numeric(m_u[3,"spending_score"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"income"]),y=as.numeric(m_u[4,"spending_score"])),color=hue_pal()(n_clusters)[4],size=5,shape=18)
## Model Based Clustering
library(mclust)
X <- dd %>% dplyr::select(age_z:genderf_z)
head(X)## age_z income_z spending_score_z genderf_z
## 1 -1.421 -1.73 -0.434 -1.125
## 2 -1.278 -1.73 1.193 -1.125
## 3 -1.349 -1.70 -1.712 0.884
## 4 -1.135 -1.70 1.038 0.884
## 5 -0.562 -1.66 -0.395 0.884
## 6 -1.206 -1.66 0.999 0.884BIC <- mclust::mclustBIC(X)
plot(BIC)
summary(BIC)## Best BIC values:
## VII,9 VII,7 VII,8
## BIC -2088 -2114.6 -2122.9
## BIC diff 0 -26.4 -34.7mod1 <- mclust::Mclust(X, x = BIC)
# this output is long, just to show that it exists
# summary(mod1, parameters = TRUE)
plot(mod1, what = "BIC")
plot(mod1, what = "classification")
# we store the model based classification
dd$mbc_9 <- mod1$classification
# we might want to inspect the cluster means in original scale
(m_u <- dd %>% dplyr::group_by(mbc_9) %>% dplyr::select(age, income, spending_score, genderf) %>% dplyr::summarize_all(mean) )## Adding missing grouping variables: `mbc_9`## # A tibble: 9 × 5
## mbc_9 age income spending_score genderf
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 45.6 27.0 20.4 0.591
## 2 2 24.1 41.5 62.7 0
## 3 3 25.5 25.7 80.5 1
## 4 4 54.2 54.2 49.0 1
## 5 5 27.5 56.9 46.7 1
## 6 6 60 54.9 49.7 0
## 7 7 33.6 81.6 83.2 0
## 8 8 31.7 82.8 81.3 1
## 9 9 40.4 90.7 25.1 0.425# we can look at classification dependent tables
table(dd$genderf, dd$mbc_9)##
## 1 2 3 4 5 6 7 8 9
## 0 9 22 0 0 0 18 16 0 23
## 1 13 0 13 26 24 0 0 19 17Segmentation Data
The dataset consists of information about the purchasing behavior of 2,000 individuals from a given area when entering a physical ‘FMCG’ store. All data has been collected through the loyalty cards they use at checkout. The data has been preprocessed and there are no missing values. In addition, the volume of the dataset has been restricted and anonymised to protect the privacy of the customers.
Variable Data type Range Description
ID numerical Integer Shows a unique identificator of a customer.
Sex categorical {0,1} Biological sex (gender) of a customer. In this dataset there are only 2 different options.
- 0 male
- 0 male
1 female
Marital status categorical {0,1} Marital status of a customer.
- 0 single
- 1 non-single (divorced / separated / married / widowed)
- 0 single
Age numerical Integer The age of the customer in years, calculated as current year minus the year of birth of the customer at the time of creation of the dataset
- 18 Min value (the lowest age observed in the dataset)
- 76 Max value (the highest age observed in the dataset)
- 18 Min value (the lowest age observed in the dataset)
Education categorical {0,1,2,3} Level of education of the customer
- 0 other / unknown
- 1 high school
- 2 university
- 3 graduate school
- 0 other / unknown
Income numerical Real Self-reported annual income in US dollars of the customer.
- 35832 Min value (the lowest income observed in the dataset)
- 309364 Max value (the highest income observed in the dataset)
- 35832 Min value (the lowest income observed in the dataset)
Occupation categorical {0,1,2} Category of occupation of the customer.
- 0 unemployed / unskilled
- 1 skilled employee / official
- 2 management / self-employed / highly qualified employee / officer
- 0 unemployed / unskilled
Settlement size categorical {0,1,2} The size of the city that the customer lives in.
- 0 small city
- 1 mid-sized city
- 2 big city
- 0 small city
Column names are changed in the example that follows
require(tidyverse)
library(scales)
set.seed(2341)
# the data come from https://www.kaggle.com/dev0914sharma/customer-clustering...
# we read from a local server for conveniance
dd <- readr::read_csv("https://md.psych.bio.uni-goettingen.de/mv/data/div/segmentation_data.csv")## Rows: 2000 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): ID, Sex, Marital status, Age, Education, Income, Occupation, Settle...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.colnames(dd) <- c("id", "genderf", "marital_status", "age", "education", "income", "occupation", "sett_size")
dd$id <- dd$id - 100000000
# we take a look at the data structure
head(dd)## # A tibble: 6 × 8
## id genderf marital_status age education income occupation sett_size
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 0 67 2 124670 1 2
## 2 2 1 1 22 1 150773 1 2
## 3 3 0 0 49 1 89210 0 0
## 4 4 0 0 45 1 171565 1 1
## 5 5 0 0 53 1 149031 1 1
## 6 6 0 0 35 1 144848 0 0# we create a standardized version of our data
# dd.z <- dd %>% dplyr::select(genderf:sett_size)
# dd.z <- data.frame(scale(dd.z))
##dd.z <- dd %>% dplyr::select(genderf:sett_size) %>% scale() %>% data.frame
##dd.z <- cbind(dd$id, dd.z)
##names(dd.z)[1] <- "id"
##head(dd.z)
dd.t <- dd %>% dplyr::select(genderf:sett_size) %>% scale() %>% data.frame()
colnames(dd.t) <- c("genderf_z", "marital_status_z", "age_z", "education_z", "income_z", "occupation_z", "sett_size_z")
dd <- cbind(dd, dd.t)
# we take a look at the data structure
head(dd)## id genderf marital_status age education income occupation sett_size genderf_z
## 1 1 0 0 67 2 124670 1 2 -0.917
## 2 2 1 1 22 1 150773 1 2 1.090
## 3 3 0 0 49 1 89210 0 0 -0.917
## 4 4 0 0 45 1 171565 1 1 -0.917
## 5 5 0 0 53 1 149031 1 1 -0.917
## 6 6 0 0 35 1 144848 0 0 -0.917
## marital_status_z age_z education_z income_z occupation_z sett_size_z
## 1 -0.993 2.6530 1.6039 0.0975 0.297 1.552
## 2 1.007 -1.1868 -0.0634 0.7825 0.297 1.552
## 3 -0.993 1.1170 -0.0634 -0.8330 -1.269 -0.910
## 4 -0.993 0.7757 -0.0634 1.3281 0.297 0.321
## 5 -0.993 1.4584 -0.0634 0.7367 0.297 0.321
## 6 -0.993 -0.0776 -0.0634 0.6270 -1.269 -0.910s.sel <- sample(dd$id, 50)
# dd.s <- dd[dd$id %in% s.sel,] %>% dplyr::select(genderf:sett_size)
dd.s <- dd[dd$id %in% s.sel,]
#dists <- dd.s %>% dist()
dists <- dd[dd$id %in% s.sel,] %>% dplyr::select(genderf:sett_size) %>% dist()
dists[1:6]## [1] 46868 61419 25071 47075 9048 33606# dists
#cutree(hclust(dists,method="single"),h=3.8)
#dd.s.z <- dd.z[dd.z$id %in% s.sel,] %>% dplyr::select(genderf:sett_size)
#dists.z <- dd.s.z %>% dist()
dists.z <- dd[dd$id %in% s.sel,] %>% dplyr::select(genderf_z:sett_size_z) %>% dist()
dists.z[1:6]## [1] 2.55 3.42 2.13 3.16 3.53 1.52# we can get cluster membership for our observations for a specific method at a specific height
cutree(hclust(dists,method="complete"),h=40000)## 21 26 52 85 127 148 150 235 239 339 364 369 428 431 473 513
## 1 2 3 4 2 1 5 2 4 1 4 1 5 1 2 1
## 532 563 591 604 629 662 731 821 923 934 1012 1090 1102 1151 1155 1158
## 5 1 4 5 5 4 5 4 4 1 3 3 4 5 5 3
## 1178 1215 1328 1365 1399 1407 1411 1504 1511 1557 1638 1666 1705 1742 1833 1862
## 1 5 2 2 1 2 4 2 5 1 1 1 4 4 1 4
## 1892 1933
## 4 1# and store it
dd.s$cu_h_40000 <- cutree(hclust(dists,method="complete"),h=40000)
# we can also store membership for a certain number of clusters
dd.s$cu_n_4 <- cutree(hclust(dists,method="complete"),k=4)
head(dd.s)## id genderf marital_status age education income occupation sett_size
## 21 21 0 0 48 1 118777 1 1
## 26 26 0 0 36 1 71909 0 0
## 52 52 0 0 30 0 180196 2 2
## 85 85 0 0 52 1 93706 0 0
## 127 127 0 1 40 1 71702 0 0
## 148 148 1 1 51 2 127825 1 0
## genderf_z marital_status_z age_z education_z income_z occupation_z
## 21 -0.917 -0.993 1.03171 -0.0634 -0.0571 0.297
## 26 -0.917 -0.993 0.00776 -0.0634 -1.2870 -1.269
## 52 -0.917 -0.993 -0.50421 -1.7306 1.5545 1.863
## 85 -0.917 -0.993 1.37302 -0.0634 -0.7150 -1.269
## 127 -0.917 1.007 0.34908 -0.0634 -1.2924 -1.269
## 148 1.090 1.007 1.28769 1.6039 0.1803 0.297
## sett_size_z cu_h_40000 cu_n_4
## 21 0.321 1 1
## 26 -0.910 2 2
## 52 1.552 3 3
## 85 -0.910 4 1
## 127 -0.910 2 2
## 148 -0.910 1 1# we can do the same with standardized cluster variables
dd.s$cz_h_5 <- cutree(hclust(dists.z,method="complete"),h=5)
# we can also store membership for a certain number of clusters
dd.s$cz_n_4 <- cutree(hclust(dists.z,method="complete"),k=4)
head(dd.s)## id genderf marital_status age education income occupation sett_size
## 21 21 0 0 48 1 118777 1 1
## 26 26 0 0 36 1 71909 0 0
## 52 52 0 0 30 0 180196 2 2
## 85 85 0 0 52 1 93706 0 0
## 127 127 0 1 40 1 71702 0 0
## 148 148 1 1 51 2 127825 1 0
## genderf_z marital_status_z age_z education_z income_z occupation_z
## 21 -0.917 -0.993 1.03171 -0.0634 -0.0571 0.297
## 26 -0.917 -0.993 0.00776 -0.0634 -1.2870 -1.269
## 52 -0.917 -0.993 -0.50421 -1.7306 1.5545 1.863
## 85 -0.917 -0.993 1.37302 -0.0634 -0.7150 -1.269
## 127 -0.917 1.007 0.34908 -0.0634 -1.2924 -1.269
## 148 1.090 1.007 1.28769 1.6039 0.1803 0.297
## sett_size_z cu_h_40000 cu_n_4 cz_h_5 cz_n_4
## 21 0.321 1 1 1 1
## 26 -0.910 2 2 2 2
## 52 1.552 3 3 1 1
## 85 -0.910 4 1 2 2
## 127 -0.910 2 2 2 2
## 148 -0.910 1 1 3 3# some linkage variants as proposed by Everitt
plot(hclust(dists, method="single"), ylab="Height", sub="Single linkage")
plot(hclust(dists, method="complete"),ylab="Height", sub="Complete linkage")
plot(hclust(dists, method="average"), ylab="Height", sub="Average linkage")
# we compare the dentrograms, both of type Complete Linkage
plot(hclust(dists, method="complete"),ylab="Height", sub="Complete linkage")
plot(hclust(dists.z, method="complete"),ylab="Height", sub="Complete linkage")
# we keep on with standardized cluster variables and create an elbow visualization,
# ... a graph to choose a suitable number of clusters
criteria <- data.frame()
nk <- 1:10
#loop for range of clusters
for (k in nk) {
model <- dd %>% dplyr::select(genderf_z:sett_size_z) %>% kmeans(centers=k, iter.max=1000, nstart=1000)
criteria <- rbind(criteria,c(k,model$tot.withinss,model$betweenss,model$totss))
}
#renaming columns
names(criteria) <- c("k","tot.withinss","betweenss","totalss")
#scree plot
ggplot(criteria, aes(x=k)) +
geom_point(aes(y=tot.withinss),color="red") +
geom_line(aes(y=tot.withinss),color="red") +
geom_point(aes(y=betweenss),color="blue") +
geom_line(aes(y=betweenss),color="blue") +
xlab("k = number of clusters") + ylab("Sum of Squares (within = red, between = blue)")
# we might vote for 4 or 5 clusters
# k-means 4 Clusters and use the scores
n_clusters = 4
model <- dd %>% dplyr::select(genderf_z:sett_size_z) %>% kmeans(centers=n_clusters, iter.max=1000, nstart=1000)
model## K-means clustering with 4 clusters of sizes 263, 570, 462, 705
##
## Cluster means:
## genderf_z marital_status_z age_z education_z income_z occupation_z
## 1 0.0901 0.391 1.6890 1.8195 0.981 0.499
## 2 -0.8573 -0.645 -0.0234 -0.5080 0.532 0.723
## 3 -0.2091 -0.954 -0.0283 -0.4856 -0.606 -0.754
## 4 0.7966 1.001 -0.5927 0.0502 -0.399 -0.276
## sett_size_z
## 1 0.457
## 2 0.965
## 3 -0.856
## 4 -0.389
##
## Clustering vector:
## [1] 1 4 3 2 2 3 2 2 1 2 4 4 4 3 4 4 3 2 1 2 2 2 3 2 2 3 3 1 2 1 2 2 2 3 4 3 2
## [38] 2 2 2 2 4 3 2 1 4 3 4 3 4 3 2 2 3 1 3 2 4 4 4 2 2 1 2 4 2 4 4 2 4 4 3 2 4
## [75] 2 1 2 2 3 4 1 2 4 1 3 4 4 2 2 2 2 2 4 2 2 1 1 2 2 2 3 3 4 2 4 2 2 2 4 4 2
## [112] 4 2 4 2 2 4 4 4 2 4 1 3 1 4 2 3 2 2 4 4 2 3 2 4 4 2 1 2 4 4 4 2 2 4 2 4 1
## [149] 2 2 3 2 2 2 2 4 2 4 2 3 2 4 2 1 2 2 4 4 4 2 3 4 2 3 2 1 1 2 2 1 2 2 3 2 2
## [186] 2 1 3 4 4 2 3 2 4 2 2 4 4 2 2 3 4 2 4 3 2 3 2 4 2 2 4 2 1 3 4 2 2 4 1 4 4
## [223] 2 2 2 2 2 2 2 2 2 3 3 4 3 2 2 1 4 2 4 2 2 4 4 2 2 3 2 4 4 4 4 2 2 3 3 2 4
## [260] 1 2 1 2 1 3 3 3 4 1 2 2 4 2 2 4 2 4 4 4 2 2 2 3 1 2 4 2 2 1 1 4 2 1 2 1 4
## [297] 4 3 2 2 4 1 3 3 2 2 4 4 4 4 3 3 4 4 3 2 3 4 2 4 2 4 2 3 4 3 2 4 2 2 1 4 2
## [334] 4 2 1 4 4 2 4 4 4 2 2 3 4 2 4 3 2 4 4 2 2 2 3 2 2 4 4 1 2 4 2 3 3 2 4 2 1
## [371] 2 2 4 1 1 4 4 2 1 4 2 1 4 2 3 4 4 2 2 4 2 4 2 4 2 2 1 1 1 4 2 4 2 3 3 4 2
## [408] 2 2 2 4 2 2 3 4 2 3 4 4 4 4 2 3 2 4 2 3 2 2 4 1 2 2 4 2 4 4 4 3 4 2 4 2 3
## [445] 2 4 4 3 1 1 2 4 2 2 2 2 2 3 4 2 2 2 4 2 2 1 4 2 4 3 4 4 3 2 4 4 3 2 3 2 4
## [482] 3 1 4 2 2 2 1 3 2 2 1 4 3 3 2 2 3 4 4 4 2 1 3 4 3 2 2 2 2 2 2 2 4 3 4 3 4
## [519] 2 2 2 4 2 4 4 2 4 3 4 3 3 4 4 4 2 2 1 4 2 4 4 1 3 3 3 2 4 2 4 2 4 3 4 2 1
## [556] 3 4 4 3 3 2 3 4 2 2 4 4 2 3 4 4 3 4 4 3 4 4 4 4 4 2 3 4 3 1 4 3 3 4 1 1 1
## [593] 4 4 2 4 4 3 3 2 1 4 4 2 4 2 1 1 2 3 4 4 4 4 4 2 2 3 4 4 2 2 2 4 1 2 2 2 2
## [630] 1 4 2 2 4 4 3 4 2 4 3 4 3 2 4 2 2 2 4 2 3 2 3 2 2 3 2 3 2 4 2 4 4 2 2 4 2
## [667] 2 4 3 3 3 2 2 2 3 4 2 4 1 4 1 2 2 1 3 2 2 2 2 2 2 4 2 3 2 3 3 4 2 2 4 2 1
## [704] 2 4 4 2 4 4 3 2 4 2 3 2 1 2 2 2 2 2 4 4 1 4 4 1 4 1 2 2 3 4 4 4 4 2 3 2 4
## [741] 2 3 2 2 2 3 4 4 3 2 1 4 4 4 2 4 1 2 3 2 1 4 3 2 2 3 4 4 2 3 4 2 2 2 1 4 2
## [778] 4 2 1 2 1 3 4 1 3 3 2 2 2 1 2 4 1 2 4 2 4 1 3 2 4 4 3 4 2 4 1 2 4 2 4 2 2
## [815] 2 1 1 4 1 2 4 2 3 3 2 4 4 2 2 2 2 4 2 1 4 2 4 4 1 1 3 3 4 3 2 3 1 4 1 3 2
## [852] 3 3 3 2 2 1 3 4 2 2 4 4 3 3 4 4 2 2 4 1 2 2 4 2 1 2 2 2 3 2 1 2 1 1 1 2 2
## [889] 2 2 2 2 3 2 2 2 4 4 4 2 2 1 2 2 2 2 3 4 4 4 4 4 4 2 3 1 3 1 2 2 4 2 4 2 1
## [926] 2 4 2 1 3 3 4 2 2 4 2 4 2 2 2 2 3 2 3 1 4 2 2 4 2 3 2 4 2 4 1 3 3 3 2 4 1
## [963] 2 3 4 4 3 1 2 3 2 3 4 2 4 1 1 2 3 2 2 2 2 2 3 4 2 1 2 3 3 3 4 2 2 4 2 2 3
## [1000] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 4 2
## [1111] 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 3 2 2 2 2 2 2 1 2 2 2 1 1 2 2 2
## [1148] 1 4 2 2 2 2 2 1 2 2 2 2 2 4 2 2 2 4 2 2 2 1 2 2 2 3 1 2 2 2 2 2 3 3 2 2 4
## [1185] 2 1 2 3 2 3 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 4 2 2 2 2 2 2 2 2
## [1222] 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 1 2 1 2 2 4 2 2 2 3 3 2 2 2 2 2 4 2 2 2 3
## [1259] 4 2 2 4 2 2 1 2 2 2 4 2 2 2 2 2 2 2 1 1 2 2 3 2 2 2 2 1 2 4 2 2 2 2 2 2 3
## [1296] 2 2 1 2 2 3 1 4 3 1 4 4 4 4 4 4 4 3 4 4 4 1 4 4 3 4 3 4 4 4 4 4 4 3 3 1 1
## [1333] 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 4 3 3 4 4 1 4 4 3 4 4 1 4 4 4 4 3 4 2 4 3
## [1370] 3 4 4 4 4 4 4 4 3 4 3 4 3 4 4 4 3 4 3 4 4 4 1 4 1 4 4 3 1 4 4 4 4 3 4 4 4
## [1407] 3 4 4 3 1 3 4 1 4 2 4 3 4 4 4 4 4 4 4 4 2 4 1 4 1 4 1 3 4 3 4 4 4 4 4 4 4
## [1444] 4 4 3 4 3 3 3 4 2 4 4 4 4 1 4 4 3 4 4 4 4 4 4 4 1 3 1 4 1 4 3 4 4 4 1 4 3
## [1481] 1 4 3 1 4 4 3 4 4 4 4 3 4 4 3 1 4 4 3 4 3 4 3 4 4 4 4 3 3 1 1 3 4 4 4 3 3
## [1518] 4 4 4 4 4 4 4 4 4 3 4 3 3 4 4 1 4 4 3 4 4 1 4 4 4 4 3 4 2 4 3 3 4 4 4 4 4
## [1555] 4 4 3 4 3 4 3 4 4 4 3 4 3 4 4 4 1 4 1 4 4 3 1 4 4 4 4 3 4 4 4 3 4 4 3 1 3
## [1592] 4 1 4 2 4 3 4 4 4 4 3 3 4 4 4 4 3 3 4 4 3 4 3 3 3 4 4 3 4 3 4 4 3 3 3 4 3
## [1629] 3 3 3 4 4 4 3 4 3 3 3 3 4 3 3 3 3 4 3 3 4 4 4 3 3 3 4 3 3 4 4 4 3 4 3 3 3
## [1666] 4 4 4 4 4 4 4 3 3 4 3 3 4 4 3 3 4 3 4 3 3 3 3 4 4 4 3 3 4 3 3 4 3 4 4 3 3
## [1703] 3 4 3 3 3 4 4 4 3 4 4 3 3 4 4 3 3 4 4 4 3 3 3 3 3 3 4 3 4 4 4 3 3 4 3 4 4
## [1740] 4 3 3 3 3 3 4 3 4 3 3 4 4 3 3 4 4 3 3 3 4 3 4 3 4 3 3 4 3 3 4 4 3 3 4 3 3
## [1777] 4 3 4 3 4 4 4 3 3 3 4 3 4 3 3 3 3 4 4 4 4 3 4 4 3 3 4 4 4 3 3 4 4 3 4 3 3
## [1814] 3 3 3 3 4 3 4 3 4 4 4 4 4 3 4 4 3 4 3 4 4 4 4 3 4 3 3 4 3 4 4 3 4 3 4 4 4
## [1851] 4 4 3 3 4 4 4 4 3 3 4 4 3 4 3 3 3 4 4 3 3 3 4 4 3 3 3 4 3 3 3 3 4 4 4 3 4
## [1888] 3 3 3 4 4 3 3 3 3 4 3 3 4 4 4 3 3 3 4 3 3 4 4 4 3 4 3 3 3 4 4 4 4 4 4 4 3
## [1925] 3 4 3 3 4 4 3 3 4 3 4 3 3 3 3 4 4 4 3 3 4 3 3 4 3 4 4 3 3 3 4 3 3 3 4 4 4
## [1962] 3 4 4 3 3 4 4 3 3 4 4 4 3 3 3 3 3 3 4 3 4 4 4 3 3 4 3 4 4 4 3 3 3 3 3 4 3
## [1999] 4 3
##
## Within cluster sum of squares by cluster:
## [1] 1688 2021 1506 1952
## (between_SS / total_SS = 48.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# if we want to use the clusters furtheron f. e. for some analyses, we store the cluster assignment
dd$kmc_4 <- factor(model$cluster)
# we store the unstandardized means of the cluster variables and take a look at it
( m_u <- dd %>% dplyr::group_by(kmc_4) %>% dplyr::select(genderf, marital_status, age, education, income, occupation, sett_size) %>% dplyr::summarize_all(mean) )## Adding missing grouping variables: `kmc_4`## # A tibble: 4 × 8
## kmc_4 genderf marital_status age education income occupation sett_size
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.502 0.692 55.7 2.13 158338. 1.13 1.11
## 2 2 0.0298 0.174 35.6 0.733 141218. 1.27 1.52
## 3 3 0.353 0.0195 35.6 0.747 97860. 0.329 0.0433
## 4 4 0.854 0.997 29.0 1.07 105759. 0.634 0.423dd %>% ggplot(aes(x=age,y=income, color=kmc_4)) +
geom_point(alpha=.6) +
geom_point(aes(x=as.numeric(m_u[1,"age"]),y=as.numeric(m_u[1,"income"])),color=hue_pal()(n_clusters)[1],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[2,"age"]),y=as.numeric(m_u[2,"income"])),color=hue_pal()(n_clusters)[2],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[3,"age"]),y=as.numeric(m_u[3,"income"])),color=hue_pal()(n_clusters)[3],size=5,shape=18) +
geom_point(aes(x=as.numeric(m_u[4,"age"]),y=as.numeric(m_u[4,"income"])),color=hue_pal()(n_clusters)[4],size=5,shape=18)
## Model Based Clustering
# source
# https://cran.r-project.org/web/packages/mclust/vignettes/mclust.html
library(mclust)
X <- dd %>% dplyr::select(age, education, income, occupation)
head(X)## age education income occupation
## 1 67 2 124670 1
## 2 22 1 150773 1
## 3 49 1 89210 0
## 4 45 1 171565 1
## 5 53 1 149031 1
## 6 35 1 144848 0# or a standardized version of it
X.z <- X %>% scale(center=TRUE, scale=TRUE)
# or less verbose
X.z <- X %>% scale()
head(X.z)## age education income occupation
## [1,] 2.6530 1.6039 0.0975 0.297
## [2,] -1.1868 -0.0634 0.7825 0.297
## [3,] 1.1170 -0.0634 -0.8330 -1.269
## [4,] 0.7757 -0.0634 1.3281 0.297
## [5,] 1.4584 -0.0634 0.7367 0.297
## [6,] -0.0776 -0.0634 0.6270 -1.269# fully explorative
mod_e <- mclust::densityMclust(X.z)
plot(mod_e, what = "BIC")
# more specific
mod <- mclust::densityMclust(X.z, G=1:5, modelNames=c("EEV", "VEV"))
plot(mod, what = "BIC")
summary(mod)## -------------------------------------------------------
## Density estimation via Gaussian finite mixture modeling
## -------------------------------------------------------
##
## Mclust VEV (ellipsoidal, equal shape) model with 3 components:
##
## log-likelihood n df BIC ICL
## -6546 2000 38 -13380 -13435dd$mclust_c <- mod$classification
table(dd$mclust_c)##
## 1 2 3
## 654 782 564# we visualize the clusters in contexts
mclust::clPairs(X.z, mod$classification)
Remark: This is the base for the sheet on cluster analysis
Modelnames finden sich in der Dokumentation mclust:
Details
The following models are available in package mclust:
univariate mixture
"E" equal variance (one-dimensional)
"V" variable/unqual variance (one-dimensional)
multivariate mixture
"EII" spherical, equal volume
"VII" spherical, unequal volume
"EEI" diagonal, equal volume and shape
"VEI" diagonal, varying volume, equal shape
"EVI" diagonal, equal volume, varying shape
"VVI" diagonal, varying volume and shape
"EEE" ellipsoidal, equal volume, shape, and orientation
"VEE" ellipsoidal, equal shape and orientation (*)
"EVE" ellipsoidal, equal volume and orientation (*)
"VVE" ellipsoidal, equal orientation (*)
"EEV" ellipsoidal, equal volume and equal shape
"VEV" ellipsoidal, equal shape
"EVV" ellipsoidal, equal volume (*)
"VVV" ellipsoidal, varying volume, shape, and orientationCheck
Idee, “interessante” Gruppeneinteilungen in den Clustervariablen zu finden und ggf. weiter zu verwenden. Beobachtungen (Vpn) clustern im Gegensatz zu FA (Variablen clustern).
Clustering braucht numerische Variablen
Gleiche Skalierung der Variablen hilft, ev. z-Transformation via
scale()Agglomerative Hierarchical Clustering explorativ, Visualisierung der Struktur, Wahl eines Cut-Off und damit Festlegung auf Clusterzahl Export von Clusterzugehörigkeiten auf bestimmtem Level oder für bestimmte Anzahl von Clustern
– K-Means Clustering Cluster-Zahl muss vorgegeben werden, Problem, diese Zahl zu finden Cluster-Zugehörigkeiten und diverse andere Infos zu Clustern werden generiert
– Modell geleitetes Clustern Modell bezieht sich auf zulässige
Clusterformen bei der Suche library(mclust) viele
Utilities, z. B. Plot über Clustervariablen hinsichtlich einer
Gruppierungsvariable via mclust::clPairs()
Zugriff auf Clusterzugehörigkeit der Beobachtungen
cutree()Interpretation der Clusterzentren charakterisiert die Beobachtungen in den Clustern. Die Clusterzentren sind die Mittelwerte der Variablen, über die die Cluster gebildet wurden, für das jeweilige Cluster. Wir suchen “charakteristische” Kombinationen von Variablenmittelwerten,
- B. “Personen mit hohem Einkommen, die verheiratet und über 60 Jahre alt sind”.
Links und Referenzen
Linkage methods explanation https://www.r-bloggers.com/2017/12/how-to-perform-hierarchical-clustering-using-r/
https://quantdev.ssri.psu.edu/tutorials/cluster-analysis-example
Ein erklärendes PDF (mathematisch)
Pasi Fränti, Sami Sieranoja, How much can k-means be improved by using better initialization and repeats? Pattern Recognition, Volume 93, 2019, Pages 95-112, https://doi.org/10.1016/j.patcog.2019.04.014.
Version: 13 Juli, 2022 18:40