K means clustering
Jhon Paul Kionesala BS Mathematics
2022-06-18
load libraries needed
suppressPackageStartupMessages(library(factoextra))
suppressPackageStartupMessages(library(cluster))load and prepare dataset
df <- USArrestsremove 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$cluster), mean)## cluster Murder Assault UrbanPop Rape
## 1 1 3.60000 78.53846 52.07692 12.17692
## 2 2 10.81538 257.38462 76.00000 33.19231
## 3 3 5.65625 138.87500 73.87500 18.78125
## 4 4 13.93750 243.62500 53.75000 21.41250The mean number of murders per 100,000 citizens among the states in cluster 1 is 3.6.
The mean number of assaults per 100,000 citizens among the states in cluster 1 is 78.6.
The mean percentage of residents living in an urban area among the states in cluster 1 is 52.1%.
The mean number of rapes per 100,000 citizens among the states in cluster 1 is 12.2. Zach (2020)
add cluster assignment to original data
final_data <- cbind(USArrests, cluster = km$cluster)
head(final_data)## Murder Assault UrbanPop Rape cluster
## Alabama 13.2 236 58 21.2 4
## Alaska 10.0 263 48 44.5 2
## Arizona 8.1 294 80 31.0 2
## Arkansas 8.8 190 50 19.5 4
## California 9.0 276 91 40.6 2
## Colorado 7.9 204 78 38.7 2