The following items are treated in the course: linear representation of multivariate data, random vectors and independence, higher order moments, gradients and optimization, learning rules for non-constrained and constrained optimization, estimation theory for signal separation, methods of least-squares and maximum likelihood, information theory, entropy cumulants, definition of PCA and ICA, differences and similarities between PCA and ICA, methods for estimation of ICA: ICA by maximization of non-Gaussianity, ICA by maximum likelihood estimation, ICA by minimization of mutual information, ICA by nonlinear decorrelation and nonlinear PCA. Applications: acoustic signal separation and deconvolution, feature extraction from multivariate data, artifact identification from EEG and MEG, prediction of time series data by using ICA.
