Hierarchical k-means clustering

The final k-means clustering solution is very sensitive to the initial random selection of cluster centers. This function provides a solution using an hybrid approach by combining the hierarchical clustering and the k-means methods. The procedure is explained in "Details" section. Read more: Hybrid hierarchical k-means clustering for optimizing clustering outputs.

• hkmeans(): compute hierarchical k-means clustering

• print.hkmeans(): prints the result of hkmeans

• hkmeans_tree(): plots the initial dendrogram

hkmeans(x, k, hc.metric = "euclidean", hc.method = "ward.D2",
  iter.max = 10, km.algorithm = "Hartigan-Wong")

# S3 method for hkmeans
print(x, ...)

hkmeans_tree(hkmeans, rect.col = NULL, ...)

Arguments

x	a numeric matrix, data frame or vector
k	the number of clusters to be generated
hc.metric	the distance measure to be used. Possible values are "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowski" (see ?dist).
hc.method	the agglomeration method to be used. Possible values include "ward.D", "ward.D2", "single", "complete", "average", "mcquitty", "median"or "centroid" (see ?hclust).
iter.max	the maximum number of iterations allowed for k-means.
km.algorithm	the algorithm to be used for kmeans (see ?kmeans).
...	others arguments to be passed to the function plot.hclust(); (see ? plot.hclust)
hkmeans	an object of class hkmeans (returned by the function hkmeans())
rect.col	Vector with border colors for the rectangles around clusters in dendrogram

Value

hkmeans returns an object of class "hkmeans" containing the following components:

• The elements returned by the standard function kmeans() (see ?kmeans)

• data: the data used for the analysis

• hclust: an object of class "hclust" generated by the function hclust()

Details

The procedure is as follow:

1. Compute hierarchical clustering

2. Cut the tree in k-clusters

3. compute the center (i.e the mean) of each cluster

4. Do k-means by using the set of cluster centers (defined in step 3) as the initial cluster centers. Optimize the clustering.

This means that the final optimized partitioning obtained at step 4 might be different from the initial partitioning obtained at step 2. Consider mainly the result displayed by fviz_cluster().

Examples

# \donttest{
# Load data
data(USArrests)
# Scale the data
df <- scale(USArrests)

# Compute hierarchical k-means clustering
res.hk <-hkmeans(df, 4)

# Elements returned by hkmeans()
names(res.hk)
#>  [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
#>  [6] "betweenss"    "size"         "iter"         "ifault"       "data"        
#> [11] "hclust"      

# Print the results
res.hk
#> Hierarchical 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  0.6950701  1.0394414  0.7226370  1.27693964
#> 3 -0.4894375 -0.3826001  0.5758298 -0.26165379
#> 4 -0.9615407 -1.1066010 -0.9301069 -0.96676331
#> 
#> Clustering vector:
#>        Alabama         Alaska        Arizona       Arkansas     California 
#>              1              2              2              1              2 
#>       Colorado    Connecticut       Delaware        Florida        Georgia 
#>              2              3              3              2              1 
#>         Hawaii          Idaho       Illinois        Indiana           Iowa 
#>              3              4              2              3              4 
#>         Kansas       Kentucky      Louisiana          Maine       Maryland 
#>              3              4              1              4              2 
#>  Massachusetts       Michigan      Minnesota    Mississippi       Missouri 
#>              3              2              4              1              2 
#>        Montana       Nebraska         Nevada  New Hampshire     New Jersey 
#>              4              4              2              4              3 
#>     New Mexico       New York North Carolina   North Dakota           Ohio 
#>              2              2              1              4              3 
#>       Oklahoma         Oregon   Pennsylvania   Rhode Island South Carolina 
#>              3              3              3              3              1 
#>   South Dakota      Tennessee          Texas           Utah        Vermont 
#>              4              1              2              3              4 
#>       Virginia     Washington  West Virginia      Wisconsin        Wyoming 
#>              3              3              4              4              3 
#> 
#> Within cluster sum of squares by cluster:
#> [1]  8.316061 19.922437 16.212213 11.952463
#>  (between_SS / total_SS =  71.2 %)
#> 
#> Available components:
#> 
#>  [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
#>  [6] "betweenss"    "size"         "iter"         "ifault"       "data"        
#> [11] "hclust"      

# Visualize the tree
hkmeans_tree(res.hk, cex = 0.6)
# or use this
fviz_dend(res.hk, cex = 0.6)


# Visualize the hkmeans final clusters
fviz_cluster(res.hk, frame.type = "norm", frame.level = 0.68)
#> Warning: argument frame.type is deprecated; please use ellipse.type instead.
#> Warning: argument frame.level is deprecated; please use ellipse.level instead.
# }