Large Scale Graph Regularized Non-Negative Matrix Factorization With ${\cal \ell}_1$ Normalization Based on Kullback–Leibler Divergence

Abstract

We propose a novel algorithm for graph regularized non-negative matrix factorization (NMF) with ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> normalization based on the Kullback-Leibler divergence. The ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> normalization is imposed to overcome the scaling ambiguity in earlier work on graph regularized NMF (GNMF) in [D. Cai, X. He, J. Han, and T. Huang, “Graph regularized non-negative matrix factorization for data representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, pp. 1548-1560, 2011]. The algorithm only involves element-wise iterative updating to ensure both non-negativity of the solution and convergence. Its element-wise structure makes the proposed algorithm suitable for large scale problems. Experiments on spoken pattern discovery on the TIDIGITS database and on image clustering of the PIE dataset show that the algorithm outperforms the previous one with a better accuracy and a lower computational complexity.