The recent development of blind signal separation techniques using computationally tractable neural network-based algoprithms such as Independent COmponent Analysis (ICA) has precipitated a revival of interest in blind signal signal separation techniques based on Maximum Likelihood (ML). ICA and similar methods rely on training networks using data whose channels each contain some mixture of `real' components deriving from an unknown model and some level of noise; the goal is to recover the real components from the mixture as faithfully as possible. We consider an alternative ML-based blind signal separation approach that uses kernel density estimators t o solve the same spearation problem. Wile several kernel density estimation methods exist, using them to perform blind signal separation has been impractical becausee their computation requires the computationally expensive evaluation of multi-dimensional integrals. We present results on our work with a new implementatioin of a ML-based kernel density estimator algorithm that uses the Epanechnikov kernel. This method avoids the costly evaluation of multi-dimensional integrals, and provides a computationally viable and practical alternative for ML-based blind signal separation. We also review some theoretical performance results on Epanechnikov kernels, and show that these are more efficient than logistic kernels from the perspective of Asymptotic Mean Integrated Squared Error. Moreover, methods using Epanechnikov kernels to solve blind signal separation problems converge more rapidly than methods using either Gassuian or gogistic kernels. In the last part of the presentation, we present an application of the proposed Epanechnikov kernel separation algorithm to the analysis of brain electric potential data and contrast its performance with ICA and representative non-statistical blind separators.
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