Fuzzy clustering for multiview data by combining latent information

Abstract

Multiview data has become very important because it is often possible to obtain multiple representations for the same set of objects. From the perspective of soft partition, this paper proposes a novel fuzzy clustering method for multiview data by combining the latent information or the membership matrices from the classical Fuzzy C-means (FCM) in each view. Considering that multiview data are generated from the same latent subspace, to assist the membership matrix in one view to explore more complementary information from other views, the proposed approach first aligns the set of membership matrices from FCMs in different views to a consensus matrix. To this end, a new objective function of fuzzy clustering is formulated and the optimization method of membership matrices is provided. Then, the optimized latent information or the membership matrix for each view is concatenated into a tensor and the final clustering is derived with the help of tensor decomposition to further exploit high order correlations between different views. To balance the importance of each view, the weighted-view version of the proposed method is also developed. In addition, we analyze the convergence of proposed methods and their computational complexity. Three experimental indices NMI, F-measure and ACC demonstrate that the proposed approach is superior to the latest multiview fuzzy clustering algorithms.