Comparison of Chernoff-type face and non-graphical methods for clustering multivariate observations

Abstract

During the past few years the use of Chernoff-type faces (a technique of representing points in k-dimensional space graphically) has been accelerating for discovering clusters and outliers present in a set of multivariate observations. However, their validation for clustering multivariate data seems to be few. The present study deals with evaluating the efficiency of Chernoff-type faces (Flury and Riedwyl) and four non-graphical algorithms, viz., ‘Single linkage’, ‘Complete linkage’, ‘Group average’ and Ward's methods for recovering true cluster structures. Four different data sets have been used, which were based on samples from mixtures of multivariate normal populations with varying variance-covariance matrix and different levels of separation factor. In order to account for the variability between the subjects, experiments with 30 subjects were conducted and they were asked to group all those faces together which look alike. The recovery of hierarchical cluster structure through Chernoff-type faces has been measured using the agreement score which is simply the number of subjects classifying the pair of faces together just by merely looking at the gestalt of a face. In all the four populations considered, the recovery of cluster structure through Chernoff-type faces using the perception matrix based on the classification of faces done by 30 subjects was more similar to that obtained by complete linkage method as evaluated by adjusted Rand statistic and Jaccard index. The efficacy of Chernoff-type faces in recovering true cluster structure seems to be poor when the classification is done by one subject only. The present study revealed that none of the subjects gave a true partitions in all the four populations considered. However, the recovery values (both adjusted Rand and Jaccard) had improved substantially when the clusters were obtained from perception matrix presenting the number of subjects who identified any two faces more similar in their gestalt.