A Deep Graph Regularized Lp Smooth Semi-Non-Negative Matrix Factorization Method for Image Clustering

Unsupervised learning often relies on non-negative matrix factorization (NMF) for extracting low-dimensional features. Standard deep NMF models, however, tend to miss complex hierarchical patterns and may warp the intrinsic geometry of high-dimensional data, resulting in solutions that are neither smooth nor stable. To counter these issues, we introduce DGLpSNMF—a deep graph-regularized Lp smooth semi-NMF—that explicitly incorporates the data’s geometric structure via graph Laplacian regularization and Lp smoothing. The optimization problem is tackled with a forward-backward splitting scheme, and we establish convergence of the generated sequence to a critical point. Experiments on four image benchmarks (JAFFE, Yale, ORL, PIE) demonstrate that DGLpSNMF consistently surpasses several state-of-the-art NMF variants in both accuracy and normalized mutual information.