Robust Nonnegative Matrix Factorization Based on Cosine Similarity Induced Metric

Abstract

Nonnegative matrix factorization (NMF) is a low-rank decomposition based image representation method under the nonnegativity constraint. However, a lot of NMF based approaches utilize Frobenius-norm or KL-divergence as the metrics to model the loss functions. These metrics are not dilation-invariant and thus sensitive to the scale-change illuminations. To solve this problem, this paper proposes a novel robust NMF method (CSNMF) using cosine similarity induced metric, which is both rotation-invariant and dilation-invariant. The invariant properties are beneficial to improving the performance of our method. Based on cosine similarity induced metric and auxiliary function technique, the update rules of CSNMF are derived and theoretically shown to be convergent. Finally, we empirically evaluate the performance and convergence of the proposed CSNMF algorithm. Compared with the state-of-the-art NMF-based algorithms on face recognition, experimental results demonstrate that the proposed CSNMF method has superior performance and is more robust to the variation of illumination.