Cluster Analysis
Winelyn Pelias
2023-04-25
Data Preparation
The built-in R dataset USArrests is used:
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 1.864967207Distance Matrix Computation and Visualization
Correlation-Based Distance Method
Alabama Alaska Arizona Arkansas California Colorado
Alabama 0.00 0.71 1.45 0.09 1.87 1.69
Alaska 0.71 0.00 0.83 0.37 0.81 0.52
Arizona 1.45 0.83 0.00 1.18 0.29 0.60
Arkansas 0.09 0.37 1.18 0.00 1.59 1.37
California 1.87 0.81 0.29 1.59 0.00 0.11
Colorado 1.69 0.52 0.60 1.37 0.11 0.00Visualize the Dissimilarity Matrix
In the plot above, similar objects are close to one another. Red color corresponds to small distance and blue color indicates big distance between observation.
Enhanced Clustering Analysis
The standard R code for computing hierarchical clustering looks like this:
Enhanced k-means Clustering
Gap Statistic Plot
Silhouette Plot
cluster size ave.sil.width
1 1 13 0.37
2 2 20 0.26
3 3 17 0.32
Optimal Number of Clusters Using Gap Statistics
[1] 3Print Result
K-means clustering with 3 clusters of sizes 13, 20, 17
Cluster means:
Murder Assault UrbanPop Rape
1 -0.9615407 -1.1066010 -0.9301069 -0.9667633
2 1.0049340 1.0138274 0.1975853 0.8469650
3 -0.4469795 -0.3465138 0.4788049 -0.2571398
Clustering vector:
Alabama Alaska Arizona Arkansas California
2 2 2 3 2
Colorado Connecticut Delaware Florida Georgia
2 3 3 2 2
Hawaii Idaho Illinois Indiana Iowa
3 1 2 3 1
Kansas Kentucky Louisiana Maine Maryland
3 1 2 1 2
Massachusetts Michigan Minnesota Mississippi Missouri
3 2 1 2 2
Montana Nebraska Nevada New Hampshire New Jersey
1 1 2 1 3
New Mexico New York North Carolina North Dakota Ohio
2 2 2 1 3
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
3 3 3 3 2
South Dakota Tennessee Texas Utah Vermont
1 2 2 3 1
Virginia Washington West Virginia Wisconsin Wyoming
3 3 1 1 3
Within cluster sum of squares by cluster:
[1] 11.95246 46.74796 19.62285
(between_SS / total_SS = 60.0 %)
Available components:
[1] "cluster" "centers" "totss" "withinss" "tot.withinss"
[6] "betweenss" "size" "iter" "ifault" "clust_plot"
[11] "silinfo" "nbclust" "data" "gap_stat" Enhanced Hierarchical Clustering
Dendrogam
Silhouette Plot
cluster size ave.sil.width
1 1 19 0.26
2 2 19 0.28
3 3 12 0.43
Scatter Plot
K-means
K-means clustering with 4 clusters of sizes 8, 13, 16, 13
Cluster means:
Murder Assault UrbanPop Rape
1 1.4118898 0.8743346 -0.8145211 0.01927104
2 -0.9615407 -1.1066010 -0.9301069 -0.96676331
3 -0.4894375 -0.3826001 0.5758298 -0.26165379
4 0.6950701 1.0394414 0.7226370 1.27693964
Clustering vector:
Alabama Alaska Arizona Arkansas California
1 4 4 1 4
Colorado Connecticut Delaware Florida Georgia
4 3 3 4 1
Hawaii Idaho Illinois Indiana Iowa
3 2 4 3 2
Kansas Kentucky Louisiana Maine Maryland
3 2 1 2 4
Massachusetts Michigan Minnesota Mississippi Missouri
3 4 2 1 4
Montana Nebraska Nevada New Hampshire New Jersey
2 2 4 2 3
New Mexico New York North Carolina North Dakota Ohio
4 4 1 2 3
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
3 3 3 3 1
South Dakota Tennessee Texas Utah Vermont
2 1 4 3 2
Virginia Washington West Virginia Wisconsin Wyoming
3 3 2 2 3
Within cluster sum of squares by cluster:
[1] 8.316061 11.952463 16.212213 19.922437
(between_SS / total_SS = 71.2 %)
Available components:
[1] "cluster" "centers" "totss" "withinss" "tot.withinss"
[6] "betweenss" "size" "iter" "ifault" "clust_plot"
[11] "silinfo" "nbclust" "data"