K-means

load libraries needed

library(factoextra)

## Loading required package: ggplot2

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(cluster)

load and prepare dataset

df <- USArrests

remove rows with missing values

df <- na.omit(df)

scale each variable to have mean of 0 and standard deviation of 1

df <- scale(df)

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  1.864967207

**Start the clustering

Since we don’t know beforehand how many clusters is optimal, we’ll create two different plots that can help us decide**

fviz_nbclust(df, kmeans, method = "wss")

• For this plot it appear that there is a bit of an elbow or “bend” at k = 4

Clusters Another way to determine the optimal number of clusters is to use a metric known as the gap statistics

calculate gap statistic based on number of clusters

gap_stat <- clusGap(df,
                    FUN = kmeans,
                    nstart = 25,
                    K.max = 10,
                    B = 50)

fviz_gap_stat(gap_stat)

• We can observe from the plot that the gap statistic is greatest at k = 4 clusters, which corresponds to the elbow strategy we employed earlier.

Perform K-Means Clustering with Optimal K

perform k-means clustering with k = 4 clusters

set.seed(1)
km <- kmeans(df, centers = 4, nstart = 25)
km

## K-means clustering with 4 clusters of sizes 13, 13, 16, 8
## 
## Cluster means:
##       Murder    Assault   UrbanPop        Rape
## 1 -0.9615407 -1.1066010 -0.9301069 -0.96676331
## 2  0.6950701  1.0394414  0.7226370  1.27693964
## 3 -0.4894375 -0.3826001  0.5758298 -0.26165379
## 4  1.4118898  0.8743346 -0.8145211  0.01927104
## 
## Clustering vector:
##        Alabama         Alaska        Arizona       Arkansas     California 
##              4              2              2              4              2 
##       Colorado    Connecticut       Delaware        Florida        Georgia 
##              2              3              3              2              4 
##         Hawaii          Idaho       Illinois        Indiana           Iowa 
##              3              1              2              3              1 
##         Kansas       Kentucky      Louisiana          Maine       Maryland 
##              3              1              4              1              2 
##  Massachusetts       Michigan      Minnesota    Mississippi       Missouri 
##              3              2              1              4              2 
##        Montana       Nebraska         Nevada  New Hampshire     New Jersey 
##              1              1              2              1              3 
##     New Mexico       New York North Carolina   North Dakota           Ohio 
##              2              2              4              1              3 
##       Oklahoma         Oregon   Pennsylvania   Rhode Island South Carolina 
##              3              3              3              3              4 
##   South Dakota      Tennessee          Texas           Utah        Vermont 
##              1              4              2              3              1 
##       Virginia     Washington  West Virginia      Wisconsin        Wyoming 
##              3              3              1              1              3 
## 
## Within cluster sum of squares by cluster:
## [1] 11.952463 19.922437 16.212213  8.316061
##  (between_SS / total_SS =  71.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

• 16states were assigned to the first cluster

• 13 states were assigned to the second cluster

• states were assigned to the third cluster

• states were assigned to the fourth cluster

plot results of final k-means model

fviz_cluster(km, data = df)

find means of each cluster

aggregate(USArrests, by=list(cluster=km$cluster), mean)

• The mean number of murders per 100,000 citizens among the states in cluster 1 is 3.6.

• The mean number of assaults per 100,000 citizens among the states in cluster 1 is 78.6.

• The mean percentage of residents living in an urban area among the states in cluster 1 is 52.1%.

• The mean number of rapes per 100,000 citizens among the states in cluster 1 is 12.2.

add cluster assignment to original data

final_data <- cbind(USArrests, cluster = km$cluster)
head(final_data)