A Converged Deep Graph Semi-NMF Algorithm for Learning Data Representation

• Published in: Circuits, systems, and signal processing Vol. 41; no. 2; pp. 1146 - 1165
• Main Authors: Huang, Haonan, Yang, Zuyuan, Li, Zhenni, Sun, Weijun
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2022; Springer Nature B.V
• Subjects: Algorithms; Automation; Circuits and Systems; Convergence; Critical point; Datasets; Decomposition; Deep learning; Electrical Engineering; Electronics and Microelectronics; Empirical analysis; Engineering; Factorization; Instrumentation; Internet of Things; Laboratories; Machine learning; Methods; Regularization; Representations; Signal processing; Signal,Image and Speech Processing; Data representation; Deep matrix factorization; Forward–backward splitting; Convergence analysis
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-021-01833-3

Deep nonnegative matrix factorization (DMF) is a particularly useful technique for learning data representation in low-dimensional space. To further obtain the complex hidden information and keep the geometrical structures of the high-dimensional data, we propose a novel deep matrix factorization model with the graph regularization (called DGsnMF). For solving the model with multi-variables, we design a forward–backward splitting scheme. After that, the convergence analysis is attached to the proposed algorithm and it is proved to converge to a critical point. Empirical experiments on benchmark datasets show that the proposed method is superior to the compared methods.