Independent Component Analysis Using Nonparametric Likelihood Ratio Criterion

Abstract

The paper presents a novel nonparametric likelihood ratio criterion for independent component analysis (ICA). This criterion is derived through a statistical hypothesis test of the independence of random variables. A likelihood ratio (LR) criterion is developed to measure the strength of independence. We accordingly estimate the unmixing matrix by maximizing the LR function and apply it to transform data into independent component space. Conventionally, the test of independence was established assuming data distributions being Gaussian, which is improper to realize ICA. To prevent assuming Gaussianity in hypothesis testing, we propose a nonparametric approach where the distributions of random variables are calculated using kernel density functions and adopted for the estimation of the LR function. Finally, a new ICA is fulfilled using the nonparametric likelihood ratio (NLR) criterion. In the experiments, we apply the proposed ICA for blind source separation and speech recognition. The evaluation of using the NLR criterion shows good performance for the separation and recognition of speech signals.