Application of Sparse Kernel Graph-regularized Discriminant Non-negative Matrix Factorization in Image Clustering

Abstract

Non-negative Matrix Factorization (NMF) is widely used in image clustering; however, it has inherent limitations, including its unsupervised nature, lack of sparsity constraints, inability to leverage label information, and difficulty in capturing the geometric structure and nonlinear characteristics of data. To address these limitations, this paper proposes a Sparse Kernel Graph-regularized Discriminant Non-negative Matrix Factorization (SKGDNMF) algorithm. The algorithm innovatively adopts a dual normalization strategy, which involves column normalization for the basis matrix and row normalization for the coefficient matrix, and integrates spectral clustering to construct an end-to-end deep clustering framework. By applying sparse regularization to the coefficient matrix, the model’s robustness is significantly improved; this regularization forms complementary optimization with graph regularization, thereby effectively alleviating overfitting. A three-dimensional golden-section parameter optimization method is employed to determine key parameters, which enhances the algorithm’s practicality. Comparative experiments conducted on multiple datasets show that SKGDNMF significantly outperforms mainstream algorithms in terms of sparsity, robustness, and clustering performance, indicating its superior effectiveness for image clustering tasks.