# Finding Clusters in Independent Component Analysis

### Francis R. Bach and Michael I. Jordan

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-02-1209

October 2002

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2002/CSD-02-1209.pdf

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.

BibTeX citation:

@techreport{Bach:CSD-02-1209, Author = {Bach, Francis R. and Jordan, Michael I.}, Title = {Finding Clusters in Independent Component Analysis}, Institution = {EECS Department, University of California, Berkeley}, Year = {2002}, Month = {Oct}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2002/5688.html}, Number = {UCB/CSD-02-1209}, 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.} }

EndNote citation:

%0 Report %A Bach, Francis R. %A Jordan, Michael I. %T Finding Clusters in Independent Component Analysis %I EECS Department, University of California, Berkeley %D 2002 %@ UCB/CSD-02-1209 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2002/5688.html %F Bach:CSD-02-1209