# Hierarchical K-Means Clustering

K-means (Chapter @ref(kmeans-clustering)) represents one of the most popular clustering algorithm. However, it has some limitations: it requires the user to specify the number of clusters in advance and selects initial centroids randomly. The final k-means clustering solution is very sensitive to this initial random selection of cluster centers. The result might be (slightly) different each time you compute k-means.

In this chapter, we described an hybrid method, named hierarchical k-means clustering (hkmeans), for improving k-means results.

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## Algorithm

The algorithm is summarized as follow:

1. Compute hierarchical clustering and cut the tree into k-clusters
2. Compute the center (i.e the mean) of each cluster
3. Compute k-means by using the set of cluster centers (defined in step 2) as the initial cluster centers

Note that, k-means algorithm will improve the initial partitioning generated at the step 2 of the algorithm. Hence, the initial partitioning can be slightly different from the final partitioning obtained in the step 4.

## R code

The R function hkmeans() [in factoextra], provides an easy solution to compute the hierarchical k-means clustering. The format of the result is similar to the one provided by the standard kmeans() function (see Chapter @ref(kmeans-clustering)).

To install factoextra, type this: install.packages(“factoextra”).

We’ll use the USArrest data set and we start by standardizing the data:

``df <- scale(USArrests)``
``````# Compute hierarchical k-means clustering
library(factoextra)
res.hk <-hkmeans(df, 4)
# Elements returned by hkmeans()
names(res.hk)``````
``````##  [1] "cluster"      "centers"      "totss"        "withinss"
##  [5] "tot.withinss" "betweenss"    "size"         "iter"
##  [9] "ifault"       "data"         "hclust"``````

To print all the results, type this:

``````# Print the results
res.hk``````
``````# Visualize the tree
fviz_dend(res.hk, cex = 0.6, palette = "jco",
rect = TRUE, rect_border = "jco", rect_fill = TRUE)``````

``````# Visualize the hkmeans final clusters
fviz_cluster(res.hk, palette = "jco", repel = TRUE,
ggtheme = theme_classic())``````

## Summary

We described hybrid hierarchical k-means clustering for improving k-means results.