Independent Components Analysis - Revealing Structure in Data
Independent Component Analysis (ICA) [1] is a statistical technique for decomposing a complex dataset into independent subparts. One common application of ICA is for solving the Blind Source Separation (BSS) problem where an observed vector signal X = AS where S is a matrix containing statistically independent components as its rows and can be thought of as the source matrix and A as the square mixing matrix.
The unknown sources are then estimated by iteratively optimising and unmixing matrix W = A-1 for example, by using the infomax algorithm [2] so that S contains mutually, statistically independent rows.
The use of ICA as a source separation technique is often illustrated with the Cocktail Party Problem, where a number of people are talking simultaneously in a room, and the listener is trying to separate one of the discussions. In this case, X would represent a multichannel recording of the sound in the room and the task for ICA would be to identify the individual speakers that each make up the rows of S.
[1] P. Comon (1994), Independent component analysis - a new concept? Signal Processing, 36:287-314.
[2] A. Bell, T. Sejnowski (1995). An information-maximisation approach to blind separation and blind deconvolution. Neural Computation, 7(6):1129-1159.