The Worse Clustering Performance Analysis

Abstract

Partitional clustering algorithms are the most widely used in pattern recognition fields. And the output of partitional clustering is sensitive to the initial parameters. Therefore, it is very important to choose the optimal parameter for a specific clustering algorithm. In the past, parameter selection usually is up to the empirically optimal clustering performance. In this paper, we propose a novel approach to parameter selection for partitional clustering based on the stability analysis of dynamical system. The main idea is as follows: any clustering algorithm can not always partition a data set into meaningful subsets, therefore the parameters corresponding to the worse clustering result should not be the optimal, especially for those corresponding to the stable worse clustering output. Such framework is called the worse clustering performance analysis. As its application, we not only present how to do parameter selection for several clustering models, but also reveal that the extreme point of its objective function does not guarantee to be the stable fixed point of this clustering algorithm. From a machine learning point of view, such conclusion means that the learning algorithm maybe not reach its original expectation under some circumstance.