An ordered subsets orthogonal nonnegative matrix factorization framework with application to image clustering

Nonnegative matrix factorization (NMF) for image clustering attains impressive machine learning performances. However, the current iterative methods for optimizing NMF problems involve numerous matrix calculations and suffer from high computational costs in large-scale images. To address this issue, this paper presents an ordered subsets orthogonal NMF framework (OS-ONMF) that divides the data matrix in an orderly manner into several subsets and performs NMF on each subset. It balances clustering performance and computational efficiency. After decomposition, each ordered subset still contains the core information of the original data. That is, blocking does not reduce image resolutions but can greatly shorten running time. This framework is a general model that can be applied to various existing iterative update algorithms. We also provide a subset selection method and a convergence analysis of the algorithm. Finally, we conducted clustering experiments on seven real-world image datasets. The experimental results showed that the proposed method can greatly shorten the running time without reducing clustering accuracy.