dendrogram is replotted, and the rect.hclust() function is used to superimpose the five-cluster solution d. The results are displayed in figure 16.3.

Sardines form their own cluster and are much higher in calcium than the other food groups. Beef heart is also a singleton and is high in protein and iron. The clam cluster is low in protein and high in iron. The items in the cluster containing beef roast to pork simmered are high in energy and fat. Finally, the largest group (mackerel to bluefish) is relatively low in iron.

Hierarchical clustering can be particularly useful when you expect nested clustering and a meaningful hierarchy. This is often the case in the biological sciences. But the hierarchical algorithms are greedy in the sense that once an observation is assigned to a cluster, it can’t be reassigned later in the process. Additionally, hierarchical clustering is difficult to apply in large samples, where there may be hundreds or even thousands of observations. Partitioning methods can work well in these situations.

16.4 Partitioning cluster analysis

In the partitioning approach, observations are divided into K groups and reshuffled to form the most cohesive clusters possible according to a given criterion. This section considers two methods: k-means and partitioning around medoids (PAM).

16.4.1K-means clustering

The most common partitioning method is the k-means cluster analysis. Conceptually, the k-means algorithm is as follows:

for (i in 2:nc){ set.seed(seed)

wss[i] <- sum(kmeans(data, centers=i)$withinss)} plot(1:nc, wss, type="b", xlab="Number of Clusters",

ylab="Within groups sum of squares")}

The data parameter is the numeric dataset to be analyzed, nc is the maximum number of clusters to consider, and seed is a random-number seed.

Let’s apply k-means clustering to a dataset containing 13 chemical measurements on 178 Italian wine samples. The data originally come from the UCI Machine Learning Repository (www.ics.uci.edu/~mlearn/MLRepository.html), but you’ll access them here via the rattle package. In this dataset, the observations represent three wine varietals, as indicated by the first variable (Type). You’ll drop this variable, perform the cluster analysis, and see if you can recover the known structure.

Listing 16.4 K-means clustering of wine data

>data(wine, package="rattle")

>head(wine)

> barplot(table(nc$Best.n[1,]),

xlab="Number of Clusters", ylab="Number of Criteria", main="Number of Clusters Chosen by 26 Criteria")

> set.seed(1234)

> aggregate(wine[-1], by=list(cluster=fit.km$cluster), mean)

Because the variables vary in range, they’re standardized prior to clustering b. Next, the number of clusters is determined using the wssplot() and NbClust() functions c. Figure 16.4 indicates that there is a distinct drop in the within-groups sum of squares when moving from one to three clusters. After three clusters, this decrease drops off, suggesting that a three-cluster solution may be a good fit to the data. In figure 16.5, 14 of 24 criteria provided by the NbClust package suggest a three-cluster solution. Note that not all 30 criteria can be calculated for every dataset.

A final cluster solution is obtained with the kmeans() function, and the cluster centroids are printed d. Because the centroids provided by the function are based on