Self-Paced Robust Sparse Non-Negative Matrix Factorization with Optimal Graph Learning

Non-negative matrix factorization (NMF) is a well-established parts-based representation learning paradigm for high-dimensional data. However, existing NMF methods often struggle to capture the intrinsic structure of data and lack sufficient robustness when dealing with corrupted data. To address these limitations, we propose a self-paced robust sparse NMF framework with optimal graph learning, termed SPRSNMF. Specifically, we integrate ℓ2,1 norm minimization with non-convex sparse regularization into a unified framework. To be specific, the ℓ2,1 norm-based reconstruction loss is utilized to enhance the robustness against noise and outliers, while ℓ2,1/2 is imposed on the representation matrix to promote sparsity. Furthermore, the self-paced learning progressively selects samples from “easy” to “hard” so that the influence of noise and outliers is suppressed during optimization. Moreover, by combining adaptive graph learning with the low-rank constraint, we derive an optimal graph learning scheme to effectively uncover the intrinsic structure of data. We develop an effective block coordinate descent (BCD) algorithm to solve the resulting non-convex optimization problem, and theoretically establish its convergence and computational complexity analysis. Extensive experiments on nine benchmark datasets from various domains demonstrate the superiority of SPRSNMF over state-of-the-art approaches.