TY - JOUR
T1 - A Progressive Hierarchical Alternating Least Squares Method for Symmetric Nonnegative Matrix Factorization
AU - Hou, Liangshao
AU - Chu, Delin
AU - Liao, Li Zhi
N1 - Funding information:
The work of Li-Zhi Liao was supported in part by under Grants HKBU12302019 and HKBU12300920 from General Research Fund (GRF) of Hong Kong. The work of Delin Chu was supported in part by NUS Research under Grants A-0004252-00-00 and A-8000430-00-00.
Publisher copyright:
© 2022 IEEE.
PY - 2023/5/1
Y1 - 2023/5/1
N2 - In this article, we study the symmetric nonnegative matrix factorization (SNMF) which is a powerful tool in data mining for dimension reduction and clustering. The main contributions of the present work include: (i) a new descent direction for the rank-one SNMF is derived and a strategy for choosing the step size along this descent direction is established; (ii) a progressive hierarchical alternating least squares (PHALS) method for SNMF is developed, which is parameter-free and updates the variables column by column. Moreover, every column is updated by solving a rank-one SNMF subproblem; and (iii) the convergence to the Karush-Kuhn-Tucker (KKT) point set (or the stationary point set) is proved for PHALS. Several synthetical and real data sets are tested to demonstrate the effectiveness and efficiency of the proposed method. Our PHALS provides better performance in terms of the computational accuracy, the optimality gap, and the CPU time, compared with a number of state-of-the-art SNMF methods.
AB - In this article, we study the symmetric nonnegative matrix factorization (SNMF) which is a powerful tool in data mining for dimension reduction and clustering. The main contributions of the present work include: (i) a new descent direction for the rank-one SNMF is derived and a strategy for choosing the step size along this descent direction is established; (ii) a progressive hierarchical alternating least squares (PHALS) method for SNMF is developed, which is parameter-free and updates the variables column by column. Moreover, every column is updated by solving a rank-one SNMF subproblem; and (iii) the convergence to the Karush-Kuhn-Tucker (KKT) point set (or the stationary point set) is proved for PHALS. Several synthetical and real data sets are tested to demonstrate the effectiveness and efficiency of the proposed method. Our PHALS provides better performance in terms of the computational accuracy, the optimality gap, and the CPU time, compared with a number of state-of-the-art SNMF methods.
KW - clustering
KW - Karush-Kuhn-Tucker points
KW - progressive hierarchical alternating least squares
KW - Symmetric nonnegative matrix factorization
UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85139396047&doi=10.1109%2fTPAMI.2022.3206465&partnerID=40&md5=0905ccca9f84a240a58d0368742282d6
U2 - 10.1109/TPAMI.2022.3206465
DO - 10.1109/TPAMI.2022.3206465
M3 - Journal article
C2 - 36103449
AN - SCOPUS:85139396047
SN - 0162-8828
VL - 45
SP - 5355
EP - 5369
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 5
ER -