Data decomposition: from independent component analysis to sparse representations

This paper provides a unifying review of some recent approaches of decomposing data, images, and signals into sets of components. We start from the classical algebraic method of singular value decomposition and then introduce principal and independent component analysis. The text continues with the main subject of this paper, sparse representation and decomposition, emphasizing their biological plausibility. In this paper emphasis will be given to the geometric perspective, with the mathematics kept to a minimum.