Hierarchical clustering with planar segments as prototypes

Abstract

Clustering methods divide a set of observations into groups in such a way that members of the same group are more similar to one another than to the members of the other groups. One of the scientifically well known methods of clustering is the hierarchical agglomerative one. For data of different properties different clustering methods appear favorable. If the data possess locally linear form, application of planar (or hyperplanar) prototypes should be advantageous. However, although a clustering method using planar prototypes, based on a criterion minimization, is known, it has a crucial drawback. It is an infinite extent of such prototypes that can result in addition of very distant data points to a cluster. Such distant points can considerably differ from the majority within a cluster. The goal of this work is to overcome this problem by developing a hierarchical agglomerative clustering method that uses the prototypes confined to the segments of hyperplanes. In the experimental part, we show that for data that possess locally linear form this method is highly competitive to the method of the switching regression models (the accuracy improvement of 24%) as well as to other well-known clustering methods (the accuracy improvement of 16%).