A network-based sparse and multi-manifold regularized multiple non-negative matrix factorization for multi-view clustering

Abstract

Multi-view clustering has attracted increasing attention in recent years since many real data sets are usually gathered from different sources or described by different feature types. Amongst various existing multi-view clustering algorithms, those that are based on non-negative matrix factorization (NMF) have exhibited superior performance. However, NMF decomposing original data directly fails to exploit global relationships between data samples and cannot be applied to datasets that are not strictly non-negative. In this paper, a network-based sparse and multi-manifold regularized multiple NMF (NSM_MNMF) for multi-view clustering is proposed, where multi-view data is transformed into multiple networks, and NMF is used to jointly factorize transformed multiple networks for capturing the shared cluster structure embedded in different views. Furthermore, sparse and multi-manifold regularization are incorporated into NMF to keep the intrinsic geometrical information of the multi-view network manifold space. Networks characterize intra-view similarity, and joint factorization reveals inter-view similarity across distinct views, while using NMF to decompose the networks instead of the original data means NSM_MNMF can be applied to datasets that are not strictly non-negative and the clustering results are interpretable. Extensive experiments are conducted on nine real data sets to assess the method proposed, and the results illustrate that NSM_MNMF outperforms other baseline approaches.