The Effect of Cluster Size, Dimensionality, and Number of Clusters on Recovery of True Cluster Structure Through Chernoff-Type Faces

Abstract

During the past few years increasing use has been made of Chernoff-type faces (a technique of graphically representing points in k-dimensional space) for discovering clusters and outliers present in a set of multivariate observations. Of late, attempts have been made to examine the validity of Chernoff-type faces as a clustering algorithm. Little is, however, known how three factors namely, cluster size, dimensionality and number of clusters affect the recovery of true cluster structure through Chernoff-type faces. The present study is addressed to this problem. Twelve data sets of the mixture of multivariate normal populations have been generated using a three-factor design ensuring the presence of a desired number of characteristics in the clusters. An experiment with 20 face-plots drawn using a CALCOMP plotter from each of the 12 simulated populations was conducted with 25 subjects. Each of the subjects was asked to group together all those faces which look alike. The study revealed that if the clusters were equal in size, the error of misclassification was minimal as compared with data sets which varied in the size of the clusters present. Furthermore, the results showed that when the number of clusters was greater, the degree of recovery of true cluster structure was also higher.