TY - GEN
T1 - An Algorithm for Randomized Nonnegative Matrix Factorization and Its Global Convergence
AU - Masuda, Takao
AU - Migita, Tsuyoshi
AU - Takahashi, Norikazu
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number JP21H03510.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Nonnegative Matrix Factorization (NMF) is to decompose a given nonnegative matrix into two nonnegative factor matrices. Recently, randomized NMF has been proposed as an approach to fast NMF of large nonnegative matrices. The main idea of this approach is to perform NMF after reducing the dimensionality of the given nonnegative matrix by multiplying it by a random matrix. Since randomized NMF is formulated as a constrained optimization problem which is slightly different from the one for original NMF, it is necessary to develop suitable algorithms for solving it. However, the conventional algorithm has a serious drawback that the constraints are not satisfied. In addition, the convergence of the algorithm has not been analyzed. In this paper, in order to overcome these drawbacks, we propose to modify the optimization problem and design an algorithm based on the hierarchical alternating least squares method to solve the modified optimization problem. We also prove the global convergence of the designed algorithm.
AB - Nonnegative Matrix Factorization (NMF) is to decompose a given nonnegative matrix into two nonnegative factor matrices. Recently, randomized NMF has been proposed as an approach to fast NMF of large nonnegative matrices. The main idea of this approach is to perform NMF after reducing the dimensionality of the given nonnegative matrix by multiplying it by a random matrix. Since randomized NMF is formulated as a constrained optimization problem which is slightly different from the one for original NMF, it is necessary to develop suitable algorithms for solving it. However, the conventional algorithm has a serious drawback that the constraints are not satisfied. In addition, the convergence of the algorithm has not been analyzed. In this paper, in order to overcome these drawbacks, we propose to modify the optimization problem and design an algorithm based on the hierarchical alternating least squares method to solve the modified optimization problem. We also prove the global convergence of the designed algorithm.
KW - Global convergence
KW - Hierarchical alternating least squares algorithm
KW - Nonnegative matrix factorization
KW - Randomized NMF
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U2 - 10.1109/SSCI50451.2021.9659900
DO - 10.1109/SSCI50451.2021.9659900
M3 - Conference contribution
AN - SCOPUS:85125785878
T3 - 2021 IEEE Symposium Series on Computational Intelligence, SSCI 2021 - Proceedings
BT - 2021 IEEE Symposium Series on Computational Intelligence, SSCI 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE Symposium Series on Computational Intelligence, SSCI 2021
Y2 - 5 December 2021 through 7 December 2021
ER -