Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representation

• URL: http://arxiv.org/abs/2405.02688v2
• Date: Sun, 27 Oct 2024 08:23:08 GMT
• Title: Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representation
• Authors: Yuheng Jia, Jia-Nan Li, Wenhui Wu, Ran Wang,
• Abstract summary: Semi-supervised symmetric non-negative matrix factorization (SNMF) We propose a novel SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation.
• Score: 27.14442336413482
• License:
• Abstract: Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available at https://github.com/JinaLeejnl/TSNMF.

Related papers

• On the Connection Between Non-negative Matrix Factorization and Latent Dirichlet Allocation [0.0]
  Non-negative matrix factorization with the generalized Kullback-Leibler divergence (NMF) and latent Dirichlet allocation (LDA) are two popular approaches for dimensionality reduction of non-negative data. We show that NMF with normalization constraints on the columns of both matrices of the decomposition and a Dirichlet prior on the columns of one matrix is equivalent to LDA.
  arXiv  Detail & Related papers  (2024-05-30T23:54:17Z)
• A Novel Maximum-Entropy-Driven Technique for Low-Rank Orthogonal Nonnegative Matrix Factorization with $\ell_0$-Norm sparsity Constraint [0.0]
  In data-driven control and machine learning, a common requirement involves breaking down large matrices into smaller, low-rank factors. This paper introduces an innovative solution to the orthogonal nonnegative matrix factorization (ONMF) problem. The proposed method achieves comparable or improved reconstruction errors in line with the literature.
  arXiv  Detail & Related papers  (2022-10-06T04:30:59Z)
• Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness [9.649070872824957]
  Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems. A new convergence analysis is provided for cubic-regularized Newton for matrix vector spaces.
  arXiv  Detail & Related papers  (2022-09-02T18:11:05Z)
• Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
  We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-05-21T01:47:17Z)
• Adversarially-Trained Nonnegative Matrix Factorization [77.34726150561087]
  We consider an adversarially-trained version of the nonnegative matrix factorization. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices.
  arXiv  Detail & Related papers  (2021-04-10T13:13:17Z)
• Self-supervised Symmetric Nonnegative Matrix Factorization [82.59905231819685]
  Symmetric nonnegative factor matrix (SNMF) has demonstrated to be a powerful method for data clustering. Inspired by ensemble clustering that aims to seek better clustering results, we propose self-supervised SNMF (S$3$NMF) We take advantage of the sensitivity to code characteristic of SNMF, without relying on any additional information.
  arXiv  Detail & Related papers  (2021-03-02T12:47:40Z)
• Clustering Ensemble Meets Low-rank Tensor Approximation [50.21581880045667]
  This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. We propose a novel low-rank tensor approximation-based method to solve the problem from a global perspective. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-12-16T13:01:37Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Fast Rank Reduction for Non-negative Matrices via Mean Field Theory [5.634825161148483]
  We formulate rank reduction as a mean-field approximation by modeling matrices via a log-linear model on structured sample space. We empirically show that our rank reduction method is faster than NMF and its popular variant, lraNMF, while achieving competitive low rank approximation error on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2020-06-09T14:55:47Z)
• Relative Error Bound Analysis for Nuclear Norm Regularized Matrix Completion [101.83262280224729]
  We develop a relative error bound for nuclear norm regularized matrix completion. We derive a relative upper bound for recovering the best low-rank approximation of the unknown matrix.
  arXiv  Detail & Related papers  (2015-04-26T13:12:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.