Xu, Y.; Lu, L.; Liu, Q.; Chen, Z. Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation. Mathematics2023, 11, 2821.
Xu, Y.; Lu, L.; Liu, Q.; Chen, Z. Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation. Mathematics 2023, 11, 2821.
Xu, Y.; Lu, L.; Liu, Q.; Chen, Z. Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation. Mathematics2023, 11, 2821.
Xu, Y.; Lu, L.; Liu, Q.; Chen, Z. Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation. Mathematics 2023, 11, 2821.
Abstract
Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph regularized Lp smooth nonnegative matrix factorization (HGSNMF), by incorporating hypergraph regularization and Lp smoothing constraint terms into the standard NMF. The hypergraph regularization term can capture the intrinsic geometry structure of the high dimension space data more comprehensively than simple graph, the Lp smoothing constraint may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of HGSNMF is theoretically investigated. The experimental results on four different data sets show that the proposed method has better clustering effect than the related state-of-the-art methods in the vast majority of cases.
Keywords
hypergraph regularization; Lp smooth; nonnegative matrix factorization; data clustering
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
