Elements discriminative non-negative matrix factorization for data clustering

Semi-supervised non-negative matrix factorization (NMF) is widely used in data clustering because it can generate more discriminative representations for high-dimensional data by leveraging partial label information. To advance research in this field, we propose a novel method, Element Discriminative NMF (EDNMF), which incorporates discrimination constraints based on the element ratio and element difference of the new representations of labeled data points. EDNMF is implemented in two variants, each with an iterative algorithm for solving the optimization problem. We further analyze the computational complexity and convergence of these algorithms. A key advantage of EDNMF is that its learned representations can serve directly as a clustering assignment matrix, thereby simplifying the clustering process. Extensive experiments on eight real-world datasets demonstrate that EDNMF consistently outperforms baseline methods, confirming its effectiveness in improving clustering performance. The code is available at https://github.com/ljisxz/EDNMF.