A Comparison of Some Methods of Cluster Analysis

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Abstract
Each individual of a multivariate sample may be represented by a point in a multidimensional Euclidean space. Cluster analysis attempts to group these points into disjoint sets which it is hoped will correspond to marked features of the sample. Different methods of cluster analysis of the same sample may assume different geometrical distributions of the points or may employ different clustering criteria or may differ in both respects. Three superficially different methods of cluster analysis are examined. It is shown that the clustering criteria of all these methods, and several new ones derived from or suggested by these methods, can be interpreted in terms of the distances between the centroids of the clusters; the geometrical point distribution is found in most instances. The methods are compared, suggestions made for their improvement, and some of their properties are established.

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