L0-Regularized Parametric Non-negative Factorization for Analyzing Composite Signals

Signal sequences are practically observed as composites in which a few number of factor signals are linearly combined with non-negative weights. Based on prior physical knowledge about the target, the factors can be modeled as parametric functions, and their parameter values benefit further analyses. In this paper, we present a novel factorization method for the composite signals in terms of parametric factor functions. The method optimizes both the factor weights and the parameter values in the factor functions. While the parameter values are simply optimized by gradient descent, we propose L₀-regularized non-negative least squares (L₀-NNLS) for optimizing the factor weights. In L₀-NNLS, both L₀ regularization and non-negativity constraint are imposed on the weights in the least squares to enhance the sparsity as much as possible. Since so regularized least squares is NPhard, we propose a stepwise forward/backward optimization to efficiently solve it in an approximated manner. Due to the sparsity by the L₀-NNLS, the proposed factorization method can automatically discover the inherent number of factor functions as well as the parametric functions themselves by estimating their parameter values. In the experiments on factorization of simulated signals and practical biological signals, the proposed method exhibits favorable performances.