Auto-weighted Multi-view Deep Non-negative Matrix Factorization with Multi-kernel Learning

Deep matrix factorization (DMF) has the capability to discover hierarchical structures within raw data by factorizing matrices layer by layer, allowing it to utilize latent information for superior clustering performance. However, DMF-based approaches face limitations when dealing with complex and nonlinear raw data. To address this issue, Auto-weighted Multi-view Deep Nonnegative Matrix Factorization with Multi-kernel Learning (MvMKDNMF) is proposed by incorporating multi-kernel learning into deep nonnegative matrix factorization. Specifically, samples are mapped into the kernel space which is a convex combination of several predefined kernels, free from selecting kernels manually. Furthermore, to preserve the local manifold structure of samples, a graph regularization is embedded in each view and the weights are assigned adaptively to different views. An alternate iteration algorithm is designed to solve the proposed model, and the convergence and computational complexity are also analyzed. Comparative experiments are conducted across nine multi-view datasets against seven state-of-the-art clustering methods showing the superior performances of the proposed MvMKDNMF.