Geometrical Interpretation of Joint Diagonalization

Abstract

Independent component analysis (ICA) is a popular approach for retrieving the independent sources generating the biomedical signals such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). Joint diagonalization (JD) of a set of target matrices, which are extracted from the biomedical signals, is one of the popular approaches for performing ICA. The main difference among the JD algorithms is the criterion which is defined to extract the demixing (diagonalizer) matrix. This paper provides a geometrical interpretation for JD helping us to propose a new set of criteria for JD which are robust against noise and quickly optimized. Simulation results demonstrate the effectiveness of the proposed criteria relative to state-of-the-art JD criteria.