Multivariate Information Bottleneck
Nir Friedman, Ori Mosenzon, Noam Slonim, Naftali Tishby
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. The information bottleneck has already been applied to document classification, gene expression, neural code, and spectral analysis. In this paper, we introduce a general principled framework for multivariate extensions of the information bottleneck method. This allows us to consider multiple systems of data partitions that are inter-related. Our approach utilizes Bayesian networks for specifying the systems of clusters and what information each captures. We show that this construction provides insight about bottleneck variations and enables us to characterize solutions of these variations. We also present a general framework for iterative algorithms for constructing solutions, and apply it to several examples.
Keywords: Clustering, Information Theory
PS Link: http://www.cs.huji.ac.il/~nir/Papers/FMST1.ps.gz
PDF Link: /papers/01/p152-friedman.pdf
AUTHOR = "Nir Friedman
and Ori Mosenzon and Noam Slonim and Naftali Tishby",
TITLE = "Multivariate Information Bottleneck",
BOOKTITLE = "Proceedings of the Seventeenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-01)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2001",
PAGES = "152--161"