Log-based sparse nonnegative matrix factorization for data representation

Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better representation. However, current NMF methods do not always generate sparse solutions. In this paper, we propose new method log-norm imposed on the factor matrices enhance sparseness. Moreover, novel column-wisely norm, named ?2,log-(pseudo) norm robustness of proposed method. The is invariant, continuous, and differentiable. ?2,log regularized shrinkage problem, derive closed-form solution, which can be used for other general problems. Efficient multiplicative updating rules are developed optimization, theoretically guarantees convergence objective value sequence. Extensive experimental results confirm method, as well enhanced sparseness robustness.