Maximum Independent Component Analysis with Application to EEG Data

Abstract

In many scientific disciplines, finding hidden influential factors behind observational data is essential but challenging. The majority of existing approaches, such as the independent component analysis (${\mathrm{ICA}}$), rely on linear transformation, that is, true signals are linear combinations of hidden components. Motivated from analyzing nonlinear temporal signals in neuroscience, genetics, and finance, this paper proposes the “maximum independent component analysis” (${\mathrm{MaxICA}}$), based on max-linear combinations of components. In contrast to existing methods, ${\mathrm{MaxICA}}$ benefits from focusing on significant major components while filtering out ignorable components. A major tool for parameter learning of ${\mathrm{MaxICA}}$ is an augmented genetic algorithm, consisting of three schemes for the elite weighted sum selection, randomly combined crossover, and dynamic mutation. Extensive empirical evaluations demonstrate the effectiveness of ${\mathrm{MaxICA}}$ in either extracting max-linearly combined essential sources in many applications or supplying a better approximation for nonlinearly combined source signals, such as $\mathrm{EEG}$ recordings analyzed in this paper.