Graph Regularized Nonnegative Matrix Factorization for Data Representation

TLDR

Matrix factorization techniques, especially Nonnegative Matrix Factorization, are widely used in information retrieval, computer vision, and pattern recognition, and data often lie on a low‑dimensional manifold in high‑dimensional space. The goal is to obtain a compact representation that reveals hidden semantics while preserving the data’s intrinsic geometric structure. Graph Regularized NMF constructs an affinity graph to encode geometry and performs factorization that respects this graph. Experiments demonstrate that GNMF outperforms state‑of‑the‑art methods on real‑world datasets.

Abstract

Matrix factorization techniques have been frequently applied in information retrieval, computer vision, and pattern recognition. Among them, Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain. On the other hand, from the geometric perspective, the data is usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space. One then hopes to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Graph Regularized Nonnegative Matrix Factorization (GNMF), for this purpose. In GNMF, an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization, which respects the graph structure. Our empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.