Independent Component Analysis

In independent component analysis (ICA), the purpose is to linearly decompose a multidimensional data vector into components that are as statistically independent as possible. For nongaussian random vectors, this decomposition is not equivalent to decorrelation as is done by principal component analysis, but something considerably more sophisticated. ICA allows one to separate nongaussian source signals from their linear mixtures 'blindly', i.e. using no other information than the congaussianity of the source signals. ICA can also be used to extract features from image and sound signals according to the principle of redundancy reduction that has its origins in the neurosciences. In my talks I will review the basic theory and theoretical background of ICA together with some recent theoretical developments.