Paper No: 145
Kernel-Based Nonlinear Independent Component Analysis
Author(s): Kun Zhang, Laiwan Chan
We propose the kernel-based nonlinear independent component analysis (ICA) method, which consists of two separate steps. First, we map the data to a high-dimensional feature space and perform dimension reduction to extract the effective subspace, which can be considered as a pre-processing step. Second, we just need to adjust a linear transformation in this subspace to make the outputs as statistically independent as possible. The advantage of this method is that it core part, the second step, is a linear problem, with the algorithm similar to traditional ICA. To overcome the ill-posedness in onlinear ICA solutions and to achieve nonlinear blind source separation (BSS), two regularization conditions are utilized. They are the smoothness regularizer and the minimal nonlinear distortion (MND) principle. The MND principle states that we would prefer the nonlinear ICA solution with the mixing system of minimal nonlinear distortion, due to the fact that in practice the nonlinearity in the data generation procedure is not very strong.