TY - JOUR
T1 - A majorization–minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization
AU - Tong, Can
AU - Wei, Jiao
AU - Qi, Shouliang
AU - Yao, Yudong
AU - Zhang, Tie
AU - Teng, Yueyang
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2023/3/15
Y1 - 2023/3/15
N2 - 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.
AB - 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.
KW - Kullback–Leibler divergence
KW - Majorization–Minimization method
KW - Nonnegative matrix factorization
KW - Orthogonal regularization
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U2 - 10.1016/j.cam.2022.114877
DO - 10.1016/j.cam.2022.114877
M3 - Article
AN - SCOPUS:85140788416
SN - 0377-0427
VL - 421
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 114877
ER -