Possibilistic c-Means Clustering Algorithms Based on Adaptive Nearest Neighbors

Possibility C-Means Clustering (PCM) removes the constraint of FCM on membership degree. However, the traditional PCM algorithm tends to encounter coincidence cluster problems during clustering, and its performance is poor when dealing with unbalanced data. To solve the problem of PCM algorithm, this paper proposes a novel algorithm called Possibilistic c-Means Clustering Algorithm Based on Adaptive Nearest Neighbors (PCM-AN). Integrating the CAN model, PCMAN introduces robustness weights to the compatibility degree between sample points and clustering centers, enhancing the local robustness of the model. Utilizing the sparse structural features of adaptive neighbors, PCM-AN emphasizes the divisibility between distinct data clusters. Consequently, PCM-AN algorithm excels in highlighting the relationship within data structures and enhancing separability among various data clusters. In this paper, an artificial two-dimensional dataset, UCI standard test datasets, and image datasets are used for experiments. The experimental results demonstrate that the clustering performance of PCM-AN algorithm has obvious advantages over other improved PCM algorithms.

I. Introduction

Clustering is a statistical method for studying classification problems with the goal of unveiling the essential structural characteristics and potential patterns within the data. With the rapid development of science and technology, clustering technology is also constantly improving, covering an increasingly wider range, including data mining [1], [2], statistics [3], spatial database technology [4], medical image segmentation [5], [6], marketing [7], and other fields. The K-means algorithm [8] is the most classic clustering method, which strives to identify tight and hyperellipsoidal clusters by iteratively optimizing an appropriate cost function. Zadeh first proposed the concept of fuzzy sets and then successfully used mathematical methods to describe fuzzy concepts, thus giving rise to fuzzy mathematics. Subsequently, James applied fuzzy set theory to cluster analysis and produced the fuzzy clustering method.