A majorization–minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization

Can Tong, Jiao Wei, Shouliang Qi, Yudong Yao, Tie Zhang, Yueyang Teng

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Nonnegative matrix factorization (NMF) is a dimension reduction and clustering technique for data analysis which has been widely used in image processing, text analysis and hyperspectral decomposition because of its stronger practical significance and better interpretability. Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal NMF (ONMF), have been shown to work remarkably better for clustering tasks than NMF. At present, a large number of algorithms have been used to solve the ONMF problems, but these methods usually cannot take into account the classification accuracy and calculation speed. In this paper, we propose a new form of penalized NMF with orthogonal regularization that combines the decomposition residual minimization based on the Euclidean distance and the orthogonality maximization based on the Kullback–Leibler divergence. This paper uses Majorization–Minimization (MM) method by minimizing a majorization function of the original problem and obtains a new iterative scheme (MM-ONMF). Comparing with several traditional ONMF methods on eight datasets, experimental results show that the proposed method has better clustering results and less computing time.

Original languageEnglish
Article number114877
JournalJournal of Computational and Applied Mathematics
Volume421
DOIs
StatePublished - 15 Mar 2023

Keywords

  • Kullback–Leibler divergence
  • Majorization–Minimization method
  • Nonnegative matrix factorization
  • Orthogonal regularization

Fingerprint

Dive into the research topics of 'A majorization–minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization'. Together they form a unique fingerprint.

Cite this