Binary Codes Based on Non-Negative Matrix Factorization for Clustering and Retrieval

Traditional non-negative matrix factorization methods cannot learn the subspace from the high-dimensional data space composed of binary codes. One hopes to discover a compact parts-based representation composed of binary codes, which can uncover the intrinsic information and simultaneously respect the geometric structure of the original data. For this purpose, we introduce discrete hashing methods and propose a novel non-negative matrix factorization to generate binary codes from the original data. In this paper, we construct an affinity graph to encode the geometrical structure of the original data, and the learned binary code subspace achieved by matrix factorization respects the structure. The proposed problem can be formulated as a mixed integer optimization problem. Therefore, we transform it into several sub-problems including an integer optimization problem, two convex problems with the non-negative constraint and a quadratic programming problem. Optimizing each sub-problem alternately until we achieve a local optimal solution. Image clustering and retrieval on image datasets show the excellent performance of our method in comparison to other dimensional reduction methods.