Kmeans_clustering_Example
AjayTalluri
January 27, 2019
K means Clustering
Clustering is the use of unsupervised techniques for grouping similar objects, Usually supervised methods use labelled objects and unsupervised methods use unlabelled objects. Clustering looks for hidden structure in the data, similarities based on attributes, It is often used for exploratory analysis and no predictions are made.
K-means Clustering
Given a collection of objects each with n measurable attributes and a chosen value k of the number of clusters, the algorithm identifies the k clusters of objects based on the objects proximity to the centres of the k groups. The algorithm is iterative with the centres adjusted to the mean of each cluster’s n-dimensional vector of attributes.
For this purpose of Week-3 Assignment I am using ‘USArrest’, Crime data analysis data which is available in R packages.
K-means clustering (MacQueen, 1967), in which, each cluster is represented by the center or means of the data points belonging to the cluster. K-medoids clustering or PAM (Partitioning Around Medoids, Kaufman & Rousseeuw, 1990), in which, each cluster is represented by one of the objects in the cluster. We’ll describe also a variant of PAM named CLARA (Clustering Large Applications) which is used for analyzing large data sets.
This particular dataset, named USArrests, contains the number of arrests for murder, assault, and rape for each of the 50 states in 1973. It also contains the percentage of people in the state who live in an urban area.
Loading Data
data("USArrests")
rawdf <- na.omit(USArrests)
head(rawdf)## Murder Assault UrbanPop Rape
## Alabama 13.2 236 58 21.2
## Alaska 10.0 263 48 44.5
## Arizona 8.1 294 80 31.0
## Arkansas 8.8 190 50 19.5
## California 9.0 276 91 40.6
## Colorado 7.9 204 78 38.7Basic Statics
Before applying K-means we can scale data using scale() function
desc_stats <- data.frame(
Min = apply(rawdf, 2, min), # minimum
Med = apply(rawdf, 2, median), # median
Mean = apply(rawdf, 2, mean), # mean
SD = apply(rawdf, 2, sd), # Standard deviation
Max = apply(rawdf, 2, max) # Maximum
)
desc_stats <- round(desc_stats, 1)
head(desc_stats)## Min Med Mean SD Max
## Murder 0.8 7.2 7.8 4.4 17.4
## Assault 45.0 159.0 170.8 83.3 337.0
## UrbanPop 32.0 66.0 65.5 14.5 91.0
## Rape 7.3 20.1 21.2 9.4 46.0df <- scale(USArrests)
head(df)## Murder Assault UrbanPop Rape
## Alabama 1.24256408 0.7828393 -0.5209066 -0.003416473
## Alaska 0.50786248 1.1068225 -1.2117642 2.484202941
## Arizona 0.07163341 1.4788032 0.9989801 1.042878388
## Arkansas 0.23234938 0.2308680 -1.0735927 -0.184916602
## California 0.27826823 1.2628144 1.7589234 2.067820292
## Colorado 0.02571456 0.3988593 0.8608085 1.864967207K means
set.seed(123)
km.res <- kmeans(scale(USArrests), 4, nstart = 25)
km.res## K-means clustering with 4 clusters of sizes 13, 16, 13, 8
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 -0.9615407 -1.1066010 -0.9301069 -0.96676331
## 2 -0.4894375 -0.3826001 0.5758298 -0.26165379
## 3 0.6950701 1.0394414 0.7226370 1.27693964
## 4 1.4118898 0.8743346 -0.8145211 0.01927104
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 4 3 3 4 3
## Colorado Connecticut Delaware Florida Georgia
## 3 2 2 3 4
## Hawaii Idaho Illinois Indiana Iowa
## 2 1 3 2 1
## Kansas Kentucky Louisiana Maine Maryland
## 2 1 4 1 3
## Massachusetts Michigan Minnesota Mississippi Missouri
## 2 3 1 4 3
## Montana Nebraska Nevada New Hampshire New Jersey
## 1 1 3 1 2
## New Mexico New York North Carolina North Dakota Ohio
## 3 3 4 1 2
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 2 2 2 2 4
## South Dakota Tennessee Texas Utah Vermont
## 1 4 3 2 1
## Virginia Washington West Virginia Wisconsin Wyoming
## 2 2 1 1 2
##
## Within cluster sum of squares by cluster:
## [1] 11.952463 16.212213 19.922437 8.316061
## (between_SS / total_SS = 71.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"aggregate(USArrests, by=list(cluster=km.res$cluster), mean)## cluster Murder Assault UrbanPop Rape
## 1 1 3.60000 78.53846 52.07692 12.17692
## 2 2 5.65625 138.87500 73.87500 18.78125
## 3 3 10.81538 257.38462 76.00000 33.19231
## 4 4 13.93750 243.62500 53.75000 21.41250Including Plots
library("factoextra")## Loading required package: ggplot2## Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZfviz_cluster(km.res, data = df,
palette = c("#00AFBB","#2E9FDF", "#E7B800", "#FC4E07"),
ggtheme = theme_minimal(),
main = "Partitioning Clustering Plot"
)
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.
Cluster Validation
library(cluster)
library(HSAUR)## Loading required package: toolsdata(pottery)
km <- kmeans(pottery,3)
dissE <- daisy(pottery)
dE2 <- dissE^2
sk2 <- silhouette(km$cl, dE2)
plot(sk2)