Information geometry of Independent Component Analysis
Speaker: Jean François Cardoso, CNRS et Institut d’Astrophysique de Paris
Independent Component Analysis is an exploratory technique which, as its name implies, aims at decomposing a vector of observations into components which are statistically independent (or as independent as possible). It has numerous applications, particularly in neurosciences for extracting brain sources from their observed mixtures collected on the scalp.
ICA goes well beyond PCA (Principal Component Analysis) because statistical independence is a much stronger property than mere decorrelation. Of course, this program implies that an ICA method must use non Gaussian statistics in order to express independence (otherwise, independence would reduce decorrelation).
In this (non technical) seminar, I use a simple construction of Information Geometry (a Pythagorean theorem in distribution space) to elucidate the connections in ICA between the main players: correlation, independence, non Gaussianity, mutual information and entropy.