On Using Quaternionic Rotations for Indpendent Component Analysis

Abstract

Independent component analysis (ICA) is a popular technique for demixing multi-sensor data. In many approaches to the ICA, signals are decorrelated by whitening data and then by rotating the result. In this paper, we introduce a four-unit, symmetric algorithm, based on quaternionic factorization of rotation matrix. It makes use an isomorphism between quaternions and $4\times 4$ orthogonal matrices. Unlike conventional techniques based on Jacobi decomposition, our method exploits 4D rotations and uses negentropy approximation as a contrast function. Compared to the widely used, symmetric FastICA algorithm, the proposed method offers a better separation quality in a presence of multiple Gaussian sources.