Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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