Online non-negative dictionary learning via moment information for sparse Poisson coding

Online dictionary learning for sparse coding is an effective tool for data analysis. It incrementally learns a set of basis vectors with sparse linear combinations of these vectors when new samples appear. Previous work assumes that the samples embed Gaussian noises, which weaken the power of these methods in handling real applications with non-negative data (e.g., frequency data in word counts). Differently, in this paper, we concentrate on online learning for non-negative dictionary by using moment information for sparse Poisson coding. We exploit the non-negativity of Poisson models to learn a set of non-negative basis vectors and a non-negative sparse linear combination for the moment information of samples. Specifically, we first formulate the online learning problem via the maximum-a-posteriori (MAP) framework. We then propose a novel online algorithm which alternatively updates the sparse-coefficient vector and the basis vectors with non-negativity constraints when a new sample arrives. More importantly, we present sufficient convergence analyses to guarantee the performance of the proposed algorithm, which leads to convergence of a stable dictionary for characterizing the moment information of samples. We finally conduct a series of experiments on word-counts data and image data to show merits of the proposed online algorithm.