On the Interface between Cluster Analysis, Principal Component Analysis, and Multidimensional Scaling

This paper shows how methods of cluster analysis, principal component analysis, and multidimensional scaling may be combined in order to obtain an optimal fit between a classification underlying some set of objects 1,…,n and its visual representation in a low-dimensional euclidean space ℝs. We propose several clustering criteria and corresponding k-means-like algorithms which are based either on a probabilistic model or on geometrical considerations leading to matrix approximation problems. In particular, a MDS-clustering strategy is presented for-displaying not only the n objects using their pairwise dissimilarities, but also the detected clusters and their average distances.