Multi-view deep reciprocal nonnegative matrix factorization

Multi-view deep matrix factorization has recently gained popularity for extracting high-quality representations from multi-view data to improve the processing performance of multi-view data in pattern recognition, data mining, and machine learning. It explores the hierarchical semantics of data by performing a multi-layer decomposition on representation matrices after decomposing the data into basis and representation matrices but ignoring the basis matrices, which also contain valuable information about data. Extracting high-quality bases during the deep representation learning process can facilitate the learning of high-quality representations for multi-view data. To this end, this paper proposes a novel deep nonnegative matrix factorization architecture, named Multi-view Deep Reciprocal Nonnegative Matrix Factorization (MDRNMF), that collaborates with high-quality basis extraction, allowing the deep representation learning and high-quality basis extraction to promote each other. Based on the representations at the top layer, this paper adaptively learns the intrinsic local similarities of data within each view to capture the view-specific information. In addition, to explore the high-order data consistency across views, this paper introduces a Schatten $p$-norm-based low-rank regularization on the similarity tensor stacked by the view-specific similarity matrices. In this way, the proposed method can effectively explore and leverage the view-specific and consistent information of multi-view data simultaneously. Finally, extensive experiments demonstrate the superiority of the proposed model over several state-of-the-art methods.