Graph Regularized Sparse Non-Negative Matrix Factorization for Clustering

The graph regularized nonnegative matrix factorization (GNMF) algorithms have received a lot of attention in the field of machine learning and data mining, as well as the square loss method is commonly used to measure the quality of reconstructed data. However, noise is introduced when data reconstr...

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Bibliographic Details
Published in:IEEE transactions on computational social systems Vol. 10; no. 3; pp. 910 - 921
Main Authors: Deng, Ping, Li, Tianrui, Wang, Hongjun, Wang, Dexian, Horng, Shi-Jinn, Liu, Rui
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Clustering
Data analysis
Data mining
Data models
Eigenvalues
Factorization
Inference
Iterative methods
Laplace equations
Linear programming
L₁-norm
Machine learning
Noise sensitivity
nonnegative matrix factorization (NMF)
Optimization
regularization
Sparse matrices
sparsity
Taylor series
ISSN:2329-924X, 2373-7476
Online Access:Get full text
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Summary:The graph regularized nonnegative matrix factorization (GNMF) algorithms have received a lot of attention in the field of machine learning and data mining, as well as the square loss method is commonly used to measure the quality of reconstructed data. However, noise is introduced when data reconstruction is performed; and the square loss method is sensitive to noise, which leads to degradation in the performance of data analysis tasks. To solve this problem, a novel graph regularized sparse NMF (GSNMF) is proposed in this article. To obtain a cleaner data matrix to approximate the high-dimensional matrix, the <inline-formula> <tex-math notation="LaTeX">l_{1} </tex-math></inline-formula>-norm to the low-dimensional matrix is added to achieve the adjustment of data eigenvalues in the matrix and sparsity constraint. In addition, the corresponding inference and alternating iterative update algorithm to solve the optimization problem are given. Then, an extension of GSNMF, namely, graph regularized sparse nonnegative matrix trifactorization (GSNMTF), is proposed, and the detailed inference procedure is also shown. Finally, the experimental results on eight different datasets demonstrate that the proposed model has a good performance.
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ISSN:2329-924X
2373-7476
DOI:10.1109/TCSS.2022.3154030