Nonnegative matrix factorization using a robust error function

Nonnegative matrix factorization (NMF) is widely used in image analysis. However, most images contain noises and outliers. Thus a robust version of NMF is needed. We propose a novel NMF using a robust error function which smoothly interpolates between the least squares at small errors and L₁-norm at large errors. An efficient computational algorithm is derived with rigorous convergence analysis. Extensive experiments are made on six image datasets to show the effectiveness of proposed approach. Robust NMF consistently provides better reconstructed images, and better clustering results as compared to standard NMF.