Penalty Constraints and Kernelization of M-Estimation Based Fuzzy C-Means

Abstract

A framework of M-estimation based fuzzy C-means clustering (MFCM) algorithm is proposed with iterative reweighted least squares (IRLS) algorithm, and penalty constraint and kernelization extensions of MFCM algorithms are also developed. Introducing penalty information to the object functions of MFCM algorithms, the spatially constrained fuzzy C-means (SFCM) is extended to penalty constraints MFCM algorithms(abbr. pMFCM).Substituting the Euclidean distance with kernel method, the MFCM and pMFCM algorithms are extended to kernelized MFCM (abbr. KMFCM) and kernelized pMFCM (abbr.pKMFCM) algorithms. The performances of MFCM, pMFCM, KMFCM and pKMFCM algorithms are evaluated in three tasks: pattern recognition on 10 standard data sets from UCI Machine Learning databases, noise image segmentation performances on a synthetic image, a magnetic resonance brain image (MRI), and image segmentation of a standard images from Berkeley Segmentation Dataset and Benchmark. The experimental results demonstrate the effectiveness of our proposed algorithms in pattern recognition and image segmentation.