Local Geometrical Deep Matrix Factorization for Multi-View Clustering.

Multi-view clustering aims to exploit information from data described by various views to optimize clustering performance. Multi-view clustering methods based on deep matrix factorization are capable of extracting intrinsic category information from data that contains a variety of knowledge. And the optimization process of deep matrix factorization suffers from several constraints. To address these issues, this paper proposes a multi-view clustering model via deep matrix factorization smoothed by local geometrical loss. Based on the assumption that samples close in original space are more likely to be in the same category, the local geometrical information is preserved during the training process of deep matrix factorization by maximizing the conditional distribution on the graphs built by different views. Then, inspired by the connection between deep auto-encoder and deep matrix factorization, we leverage a deep auto-encoder based solution to handle the optimization of the objective function. By adding an activation function to each layer of deep auto-encoders, the nonnegativity of features output from layers in deep matrix factorization is strictly guaranteed during the training process. Finally, we conduct extensive experiments on four datasets to validate that the proposed method is superior to state-of-the-arts.