Deep Robust Nonnegative Matrix Factorization for Hierarchical Data Representation

ABSTRACT

In complex, real‐world scenarios, datasets frequently exhibit the presence of noise, outliers and various disturbances, posing significant challenges for effective data representation and feature extraction. In this paper, we employ a hierarchical structure in the nonnegative matrix factorization algorithm to improve the extraction of meaningful features. The proposed algorithm employs a loss function grounded in the ‐norm, which has been shown to be particularly effective in mitigating the effects of noise and outliers. The incorporation of orthogonality regularization serves to facilitate the extraction of distinct and non‐redundant features. We derive the multiplicative iterative formula necessary for addressing the associated constrained optimization problem and theoretically guarantee its local convergence by proving the monotonicity and boundedness of the objective function. Empirical evaluations conducted on six standard benchmark datasets illustrate that our proposed algorithm outperforms several existing classical methods, yielding more robust and discriminative features.