288 pp. per issue
6 x 9, illustrated
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Neural Computation

April 2009, Vol. 21, No. 4, Pages 1145-1172
(doi: 10.1162/neco.2008.12-06-421)
© 2008 Massachusetts Institute of Technology
Bayesian k-Means as a “Maximization-Expectation” Algorithm
Article PDF (390.53 KB)

We introduce a new class of “maximization-expectation” (ME) algorithms where we maximize over hidden variables but marginalize over random parameters. This reverses the roles of expectation and maximization in the classical expectation-maximization algorithm. In the context of clustering, we argue that these hard assignments open the door to very fast implementations based on data structures such as kd-trees and conga lines. The marginalization over parameters ensures that we retain the ability to infer model structure (i.e., number of clusters). As an important example, we discuss a top-down Bayesian k-means algorithm and a bottom-up agglomerative clustering algorithm. In experiments, we compare these algorithms against a number of alternative algorithms that have recently appeared in the literature.