[Lisa_seminaires] REMINDER: UdeM-McGill-MITACS machine learning seminar, PAA 1409 (UdeM), Fri Sept 28, 11:30am]
Hugo Larochelle
larocheh at IRO.UMontreal.CA
Thu Sep 27 16:32:45 EDT 2007
This week's seminar (see http://www.iro.umontreal.ca/article.php3?id_article=107&lang=en):
How Many Clusters? An Information-Theoretic Perspective
by Susanna Still,
Department of Information and Computer Sciences
University of Hawaii
Location: Pavillon Andre-Aisenstadt (UdeM), room 1409
Time: September 28th 2007, 11h30
Clustering provides a common means of identifying structure
in complex data, and there is renewed interest in clustering
as a tool for the analysis of large data sets in many fields.
Anatural question is how many clusters are appropriate for
the description of a given system. Traditional approaches to
this problem are based on either a framework in which clusters
of a particular shape are assumed as a model of the system or
on a two-step procedure in which a clustering criterion determines
the optimal assignments for a given number of clusters and a
separate criterion measures the goodness of the classification
to determine the number of clusters. In a statistical mechanics
approach, clustering can be seen as a trade-off between energy-
and entropy-like terms, with lower temperature driving the
proliferation of clusters to provide a more detailed description
of the data. For finite data sets, we expect that there is a
limit to the meaningful structure that can be resolved and
therefore a minimum temperature beyond which we will capture
sampling noise. This suggests that correcting the clustering
criterion for the bias that arises due to sampling errors will
allow us to find a clustering solution at a temperature that is
optimal in the sense that we capture maximal meaningful
structure-without having to define an external criterion for
the goodness or stability of the clustering. We show that in a
general information-theoretic framework, the finite size of a
data set determines an optimal temperature, and we introduce a
method for finding the maximal number of clusters that can be
resolved from the data in the hard clustering limit.
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