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Bayesian k-Means as a "maximization-expectation" algorithm.

Kenichi Kurihara1, Max Welling

  • 1Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan. kurihara@mi.cs.titech.ac.jp

Neural Computation
|February 10, 2009
PubMed
Summary
This summary is machine-generated.

We introduce novel maximization-expectation (ME) algorithms for clustering. These algorithms efficiently infer model structure and number of clusters, outperforming existing methods in experiments.

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Area of Science:

  • Machine Learning
  • Data Mining
  • Computational Statistics

Background:

  • The Expectation-Maximization (EM) algorithm is a standard for statistical model estimation.
  • Classical EM alternates between expectation and maximization steps.
  • Limitations exist in EM's direct application to certain clustering problems and model selection.

Purpose of the Study:

  • Introduce a new class of "maximization-expectation" (ME) algorithms.
  • Reverse the roles of expectation and maximization compared to classical EM.
  • Develop fast clustering algorithms capable of inferring model structure.

Main Methods:

  • ME algorithms maximize over hidden variables and marginalize over random parameters.
  • Utilize efficient data structures like kd-trees for hard assignments.
  • Implement Bayesian k-means and agglomerative clustering algorithms as examples.

Main Results:

  • ME algorithms enable very fast clustering implementations.
  • Marginalization over parameters facilitates inference of model structure (e.g., number of clusters).
  • Experimental comparisons show competitive or superior performance against alternative algorithms.

Conclusions:

  • ME algorithms offer a powerful alternative to classical EM for clustering.
  • The proposed methods provide efficient and effective solutions for unsupervised learning.
  • Future work can explore broader applications of ME algorithms in statistical modeling.