A Novel Adaptive Possibilistic Clustering Algorithm

Abstract

In this paper a novel possibilistic c-means clustering algorithm, called Adaptive Possibilistic c-means, is presented. Its main feature is that its parameters, after their initialization, are properly adapted during its execution. Provided that the algorithm starts with a reasonable overestimate of the number of physical clusters formed by the data, it is capable, in principle, to unravel them (a long-standing issue in the clustering literature). This is due to the fully adaptive nature of the proposed algorithm that enables the removal of the clusters that gradually become obsolete. In addition, the adaptation of all its parameters increases the flexibility of the algorithm in following the variations in the formation of the clusters that occur from iteration to iteration. Theoretical results that are indicative of the convergence behavior of the algorithm are also provided. Finally, extensive simulation results on both synthetic and real data highlight the effectiveness of the proposed algorithm.

Sparsity-Aware Possibilistic Clustering Algorithms

“…This will allow the algorithm to track the changes occuring in the formation of clusters during its execution. Such a method has been proposed in [15], where a PCM algorithm called adaptive PCM (APCM) was introduced. As shown in [15], besides the above, APCM is able to determine the true number of clusters.…”

“…Such a method has been proposed in [15], where a PCM algorithm called adaptive PCM (APCM) was introduced. As shown in [15], besides the above, APCM is able to determine the true number of clusters. In the sequel, we extend SPCM in order to incorporate the adaptation of γ j 's by embedding the relevant mechanism of APCM.…”

“…As a consequence of the above, the algorithm inherits the ability to detecting automatically also the true number of physical clusters. Next, inspired by [15], we describe how the parameters γ j 's are adapted in SAPCM, so that starting from an overestimated number of clusters, to conclude to the true number of physical clusters.…”

“…with η j being a measure of the mean absolute deviation of C j as it has been formed in the current iteration (to be defined rigorously in the next subsection), α is a user-defined positive parameter [15] andη is a constant defined as the minimum among all initial η j 's, i.e.,η = min j=1,...,mini η j , where m ini is the initial number of clusters.…”

“…In order to deal with the problem of the estimation of the parameters involved in PCMs, the SPCM is further extended using the rationale proposed in [15], based on which these parameters are properly adjusted during the execution of the algorithm. Such an extension gives rise to the so called Sparse Adaptive PCM (SAPCM) algorithm 2 .…”