Local independent component analysis by the self-organizing map

Abstract

We introduce a neural network for the analysis of local independent components of an input signal. The network is a modification of Kohonen's adaptive-subspace self-organizing map. The map units consist of weight matrices adapted to represent linear transformations which locally minimize statistical dependence among pattern vector components. Training of the map is carried out in episodes comprising pattern vectors sampled from adjacent time instants or spatial locations. The use of episodes produces independent directions which are preserved in translations of the input signal. The independent components modeled by each map unit are estimated with a nonlinear Hebbian-like learning rule, which searches for weight vectors maximizing a measure of non-Gaussianity of the scalar product of weight and pattern vectors. For demonstration, the method was applied to the segmentation of a composition image of four periodic texture fields. The spatial convolution masks, created by the map for the extraction of independent components, represent distinct frequences of particular directions.