Regularized Discriminant in the Setting of Fuzzy c-Means Classifier

A fuzzy c-means classifier derived from a viewpoint of iteratively reweighted least square techniques (IRLS-FCM) has been proposed, in which membership functions are variously chosen and parameterized. This paper focuses on the postsupervised classifier design and three kinds of regularization methods for classification are addressed: 1) the exponent of membership function or weights in entropy term in the FCM clustering, 2) the modification of covariance matrices in defining Mahalanobis distances and 3) the designing of intermediate classification rules between linear and quadratic in the regularized discriminant analysis (RDA). We test the efficiency of these regularization methods in the IRLS-FCM classifier with regard to its performance and data set compression ratio, and show the best parameter values. Among the three regularization approaches, the improvement in classification performances is achieved mostly by the methods 1) and 2). Experiments on several well-known benchmark data sets, shows that the FCM classifier using a newly defined membership function outperforms well-established prototype-based methods, i.e., k-nearest neighbor classier (k-NN) and learning vector quantization (LVQ). Also concerning storage requirements and classification speed, the IRLS-FCM classifier gives a good performance and efficiency.