Evolutionary Based ICA With Reference for EEG <inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math> </inline-formula> Rhythm Extraction

Abstract

Independent component analysis with reference (ICA-R), a paradigm of constrained ICA (cICA), incorporates textita priori information about the desired sources as reference signals into the contrast function of ICA. Reference signals direct the search toward the separation of desired sources more efficiently and accurately than the ICA. The penalized contrast function of ICA-R is non-smooth everywhere and the ICA-R algorithm does not always reach the global optimum due to the Newton-like learning used. In this paper, we propose a constrained differential evolutionary algorithm with an improved initialization strategy to solve the constrained optimization problem of ICA-R that can asymptotically converge to the optimum. It completely avoids the formulation of a penalized contrast function and scaling (due to the Lagrangian multipliers) by incorporating the ICA contrast function and the violation of the closeness constraint into the selection process of the evolution. Experiments with synthetic data and isolation of $\mu $ rhythmic activity from EEG showed improved source extraction performance over ICA-R and its recent enhancements.