Double indices induced FCM clustering and its integration with fuzzy subspace clustering

Fuzzy c-means is one of the most popular algorithms for clustering analysis. In this study, a novel FCM based algorithm called double indices induced FCM (DI-FCM) is developed from a new perspective. DI-FCM introduces a power exponent r into the constraints of the objective function such that the range of the fuzziness index m is extended. Furthermore, it can be explained from the perspective of entropy concept that the power exponent r facilitates the introduction of entropy based constraints into fuzzy clustering algorithms. As an attractive and judicious application, DI-FCM is integrated with the fuzzy subspace clustering (FSC) algorithm so that a novel subspace clustering algorithm called double indices induced fuzzy subspace clustering (DI-FSC) algorithm is proposed for high dimensional data. In DI-FSC, the commonly-used Euclidean distance is replaced by the feature-weighted distance, which results in two fuzzy matrices in the objective function. Meanwhile, the convergence property of DI-FSC is also investigated. Experiments on the artificial data as well as the real text data were conducted and the experimental results show the effectiveness of the proposed algorithm.