2021/03/24 by Mulin Chen, Xuelong Li, Chen, Mulin +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Social Sciences · #Advanced Computing and Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Face and Expression Recognition #Gene expression and cancer classification #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2103.13487
openalex publication_date 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal centroids by minimizing the sum of the approximation errors. However, the outliers deviating from the normal data distribution may have large residues, and then dominate the objective value seriously. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization, which minimizes the entropy of the residue distribution and allows a few samples to have large approximation errors. In this way, the outliers do not affect the approximation of the normal samples. The multiplicative updating rules for EMMF are also designed, and the convergence is proved both theoretically and experimentally. In addition, a Graph regularized version of EMMF (G-EMMF) is also presented to deal with the complex data structure. Clustering results on various synthetic and real-world datasets demonstrate the reasonableness of the proposed models, and the effectiveness is also verified through the comparison with the state-of-the-arts.