Polynomial Networks Representation of Nonlinear Mixtures with Application in Underdetermined Blind Source Separation
Lu Wang, Tomoaki Otsuki Ohtsuki · 2019
Similar to the deep architectures, a novel multi-layer architecture is used to extend the linear blind source separation (BSS) method to the nonlinear case in this paper. The approach approximates the nonlinearities based on a polynomial network, where the layer of our network begins with the polynomial of degree 1, up to build an output layer that can represent data with a small bias by a good approximate basis. Relying on several transformations of the input data, with higher-level representation from lower-level ones, the networks are to fulfill a mapping implicitly to the high-dimensional space. Once the polynomial networks are built, the coefficient matrix can be estimated by solving an l1-regularization on the coding coefficient vector. The experiment shows that the proposed approach exhibits a higher separation accuracy than the comparison algorithms.