Robust Non-negative Matrix Factorization with Supervised Graph Embedding for Image Classification

• Minghua Wan,
• Weiyu Gu,
• Guowei Yang,
• Hai Tan,

Vol. 19, No. 3, March 31, 2025
10.3837/tiis.2025.03.013, Download Paper (Free):

• Non-negative Matrix Factorization
• L2
• 1-norm
• supervised weight matrix
• Image Classification
• robustness

Abstract

In recent years, non-negative matrix factorization (NMF) methods based on graph embedding have been widely applied in the field of image classification. Despite their significant success, these methods have some limitations: 1) Existing methods are sensitive to noise interference and occlusion; 2) They do not fully account for intra-class compactness and inter-class separability; 3) Some models arbitrarily assume that the subspace distribution of samples within the same class is identical; 4) Traditional graph embedding methods often necessitate the introduction of additional regularization parameters, thereby reducing the algorithm's interpretability. To address these issues, this paper proposes a novel method called robust non-negative matrix factorization with supervised graph embedding (RNMF-SGE). RNMF-SGE integrates label information, graph embedding structures, ℓ2,1-norm sparsity constraint, and NMF method into a unified optimization framework. Firstly, we employ ℓ2,1-norm constraint to reduce sensitivity to noise interference. Secondly, we utilize a weight matrix to ensure that the subspace distribution of samples within the same class is similar but not necessarily identical. To fully consider intra-class compactness and inter-class separability, we impose constraints on the learning of the weight matrix using label information. Lastly, to avoid introducing additional regularization terms, we integrate the supervised weight matrix into the NMF model in a parameter-free manner. Comprehensive experiments demonstrate that RNMF-SGE exhibits enhanced robustness, superior classification performance, and improved generalization capability compared to a series of advanced NMF algorithms.

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