Abstract
Independent component analysis (ICA) is a popular technique for demixing multi-channel data. The performance of typical ICA algorithm strongly depends on many factors such as the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often a linear mixing model is assumed and the source signals are extracted by proceeding data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a four-unit, symmetric algorithm, based on the quaternionic factorization of the rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits 4 x 4 rotation matrices and uses negentropy approximation as a contrast function. Consequently, the proposed method can be adapted to a given data distribution (e.g. super-Gaussians) by selecting the appropriate non-linear function that approximates the negentropy. Compared to the widely used, symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and offers better numerical stability in the presence of multiple Gaussian sources.
Linear Independent Component Analysis Over Finite Fields: Algorithms and Bounds