Clustering Incomplete Data Using Kernel-Based Fuzzy C-means Algorithm

Abstract

There is a trend in recent machine learning community to construct a nonlinear version of a linear algorithm using the 'kernel method', e.g. Support Vector Machines (SVMs), kernel principal component analysis, kernel fisher discriminant analysis and the recent kernel clustering algorithms. In unsupervised clustering algorithms using kernel method, typically, a nonlinear mapping is used first to map the data into a potentially much higher feature space, where clustering is then performed. A drawback of these kernel clustering algorithms is thatthe clustering prototypes lie in high dimensional feature space and hence lack clear and intuitive descriptions unless using additional projection approximation from the feature to the data space as done in the existing literatures. In this paper, a novel clustering algorithm using the 'kernel method' based on the classical fuzzy clustering algorithm (FCM) is proposed and called as kernel fuzzy c-means algorithm (KFCM). KFCM adopts a new kernel-induced metric in the data space to replace the original Euclidean norm metric in FCM and the clustered prototypes still lie in the data space so that the clustering results can be reformulated and interpreted in the original space. Our analysis shows that KFCM is robust to noise and outliers and also tolerates unequal sized clusters. And finally this property is utilized to cluster incomplete data. Experiments on two artificial and one real datasets show that KFCM hasbetter clustering performance and more robust than several modifications of FCM for incomplete data clustering.