Clustering performance of different density function weighted FCM algorithm

Fuzzy C-Means (FCM) algorithm is an unsupervised fuzzy clustering method. Clustering results accuracy of the algorithm is affected by equal partition trend of the data sets. When amount of each cluster sample are difference greatly, the optimal solution of the algorithm may not be the correct partition of the data sets. Weighted Fuzzy C-Means (WFCM) algorithm is proposed to overcome this disadvantage. The WFCM algorithm contained a density function which calculates density of each sample by Gaussian function or reciprocal of distance function. The density function solves the problem of equal partition trend to some extent, and also retains favorable convergence and stability for the FCM algorithm. The experiment results are evaluated by the cluster indexes, such as partition coefficient, partition entropy and Xie-Beni index. It shows which weighted function improves the clustering performance of the WFCM algorithm better. When partially supervised information obtained from a few labeled samples is introduced to the WFCM algorithm, the clustering performance of the WFCM algorithm is further enhanced and the convergent speed of objective function is further accelerated.

I. Introduction

The FCM algorithm is the most popular one in the field of fuzzy clustering. The algorithm is an extension of the classical and the crisp clustering in fuzzy set domain. The method was widely studied and applied in pattern recognition, image processing, data mining, and so on. But clustering precision of the algorithm is affected by its equal partition trend for data sets. The optimum clustering result of the FCM algorithm may not be a correct partition for data sets being large discrepancy of every class samples number in [1]. To overcome the equal partition trend, a more effective FCM algorithm, density function weighted FCM algorithm, is proposed in this paper. The weighted function of the WFCM algorithm is produced to calculate density of each sample by density function, such as Gaussian function, or reciprocal of distance function.