title: Dependency reduction with divisive normalization: justification and effectiveness.
abstract: Efficient coding transforms that reduce or remove statistical dependencies in natural sensory signals are important for both biology and engineering. In recent years, divisive normalization (DN) has been advocated as a simple and effective nonlinear efficient coding transform. In this work, we first elaborate on the theoretical justification for DN as an efficient coding transform. Specifically, we use the multivariate t model to represent several important statistical properties of natural sensory signals and show that DN approximates the optimal transforms that eliminate statistical dependencies in the multivariate t model. Second, we show that several forms of DN used in the literature are equivalent in their effects as efficient coding transforms. Third, we provide a quantitative evaluation of the overall dependency reduction performance of DN for both the multivariate t models and natural sensory signals. Finally, we find that statistical dependencies in the multivariate t model and natural sensory signals are increased by the DN transform with low-input dimensions. This implies that for DN to be an effective efficient coding transform, it has to pool over a sufficiently large number of inputs.
authors.affiliation: Computer Science Department, University at Albany, State University of New York, Albany, NY 12222, USA. lsw@cs.albany.edu
authors.forename: Siwei
authors.initials: S
authors.lastname: Lyu
mesh_terms: D000818:Animals; D001921:Brain / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics