Accelerated sparse nonnegative matrix factorization for unsupervised feature learning

Sparse Nonnegative Matrix Factorization (SNMF) is a fundamental unsupervised representation learning technique, and it represents low-dimensional features of a data set and lends itself to a clustering interpretation. However, the model and algorithm of SNMF have some shortcomings. In this work, we created a clustering method by improving the SNMF model and its Alternating Direction Multiplier Method acceleration algorithm. A novel, fast and closed-form iterative solution is proposed for SNMF with implicit sparse constraints which are L- 1 and L-2 norms of the coefficient and basis matrixes, respectively. A low-dimensional feature space is also proposed as result of the closed-form iteration formats of each sub-problem obtained by variable splitting. In addition, the convergence points of the presented iterative algorithms are stationary points of the model. Finally, numerical experiments show that the improved algorithm is comparable to the sate-of-the-art methods in data clustering. (C) 2022 Elsevier B.V. All rights reserved.