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An MDL Framework for Data Clustering
Petri Kontkanen, Petri Myllymäki, Wray Buntine, Jorma Rissanen and Henry Tirri
In:
Advances in Minimum Description Length: Theory and Applications
(2005)
MIT Press
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AbstractWe regard clustering as a data assignment problem where the goal is to
partition the data into several non-hierarchical groups of items. For
solving this problem, we suggest an information-theoretic framework
based on the minimum description length (MDL) principle. Intuitively,
the idea is that we group together those data items that can be
compressed well together, so that the total code length over all the
data groups is optimized. One can argue that as efficient compression
is possible only when one has discovered underlying regularities that
are common to all the members of a group, this approach produces an
implicitly defined similarity metric between the data items. Formally
the global code length criterion to be optimized is defined by using
the intuitively appealing universal normalized maximum likelihood code
which has been shown to produce optimal compression rate in an
explicitly defined manner. The number of groups can be assumed to be
unknown, and the problem of deciding the optimal number is formalized
as part of the same theoretical framework. In the empirical part of
the paper we present results that demonstrate the validity
of the suggested clustering framework.
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