Finding Clusters in Independent Component Analysis
Abstract: We present a class of algorithms that find clusters in independent component analysis (ICA): the data are linearly transformed so that the resulting components can be grouped into clusters, whose elements are dependent and are independent from variables in different clusters. In order to find such clusters, we look for a transform that fits the estimated sources to a forest-structured graphical model. In the non-Gaussian, temporally independent case, the optimal transform is found by minimizing a contrast function based on mutual information that directly extends the contrast function used for classical ICA. We also derive a contrast function in the Gaussian stationary case that is based on spectral densities and generalizes the contrast function of Pham to richer classes of dependency.