Learning Nonlinear Overcomplete Representations for Efficient Coding

We derive a learning algorithm for inferring an overcomplete basis by viewing it as probabilistic model of the observed data. Over(cid:173) complete bases allow for better approximation of the underlying statistical density. Using a Laplacian prior on the basis coefficients removes redundancy and leads to representations that are sparse and are a nonlinear function of the data. This can be viewed as a generalization of the technique of independent component anal(cid:173) ysis and provides a method for blind source separation of fewer mixtures than sources. We demonstrate the utility of overcom(cid:173) plete representations on natural speech and show that compared to the traditional Fourier basis the inferred representations poten(cid:173) tially have much greater coding efficiency.