Title: A description length approach to determining the number of k-means clusters,
Abstract: We present an asymptotic criterion to determine the optimal number of
clusters in k-means. We consider k-means as data compression, and propose to
adopt the number of clusters that minimizes the estimated description length
after compression. Here we report two types of compression ratio based on two
ways to quantify the description length of data after compression. This
approach further offers a way to evaluate whether clusters obtained with
k-means have a hierarchical structure by examining whether multi-stage
compression can further reduce the description length. We applied our criteria
to determine the number of clusters to synthetic data and empirical
neuroimaging data to observe the behavior of the criteria across different
types of data set and suitability of the two types of criteria for different
datasets. We found that our method can offer reasonable clustering results that
are useful for dimension reduction. While our numerical results revealed
dependency of our criteria on the various aspects of dataset such as the
dimensionality, the description length approach proposed here provides a useful
guidance to determine the number of clusters in a principled manner when
underlying properties of the data are unknown and only inferred from
observation of data.