Robust Non-Negative Matrix Tri-Factorization with Dual Hyper-Graph Regularization

doi:10.26599/BDMA.2024.9020055

Robust Non-Negative Matrix Tri-Factorization with Dual Hyper-Graph Regularization

2025-02-01

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DOI：10.26599/BDMA.2024.9020055

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Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l(2,1)-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cuttina-edae alaorithms across seven datasets corrupted with four types of noise.

Keywords:

Noise

Clustering algorithms

Machine learning

Big Data

Benchmark testing

Robustness

Data mining

Computational complexity

Convergence

Non-negative Matrix Tri-Factorization (NMTF)

l(2,1)-norm

dual hyper-graph regularization

co-clustering

Robust Non-Negative Matrix Tri-Factorization with Dual Hyper-Graph Regularization

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