PCA Based Hierarchical Clustering with Planar Segments as Prototypes and Maximum Density Linkage

Abstract

Clustering is an indispensable tool for finding natural boundaries among data. One of the most popular methods of clustering is the hierarchical agglomerative one. For data of different properties different versions of hierarchical clustering appear favorable. If the data possess locally linear form, application of hyperplanar prototypes should be advantageous. However, although a clustering method using planar prototypes, based on hierarchical agglomerative clustering with maximum density of planar segment linkage is known, it has a crucial drawback. It uses linear regression to model a cluster. When data for a cluster are parallel to the independent variable axis the use of linear regression can not be effective and the data are not described well. As a result, quality of the obtained group is low. The goal of this work is to overcome this problem by developing a hierarchical agglomerative clustering method that uses the PCA based maximum density of planar segment linkage. In the experimental part, we show that for data that possess locally linear form this method is competitive to the method of the agglomerative hierarchical clustering based on the maximum density of planar segment linkage.