A New Hierarchical Procedure for Natural Groups Identification in Euclidean Space

Abstract

In this work we discuss the Natural Group Problem (NP-Complete), where we evaluate some non hierarchical methods by a parallel implementation of a categorization process that uses the index of Calinski & Harabasz in conjunction with algorithms of Means (H-Means). After having observed that this method did not obtain good results, we were stimulated to develop a new methodology for natural groups identification based on hierarchical techniques. We found and show important properties in the hierarchical identification of natural groups. Starting from these properties, we built a new polynomial algorithm- O(n 2 log n), based on simple criteria we call NGI (Natural Group Identification Procedure). The procedure returns better than the first we evaluate, and outperforms some other methods from the literature. We show in our tests that it reaches exact solutions for a number of Euclidean examples (ℜ 2) tested, using data sets from the literature. All the results were investigated using the SCLUSTER system, built to facilitate multivariate analysis tasks