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Mixture Complexity and Its Application to Gradual Clustering Change Detection.

Shunki Kyoya1, Kenji Yamanishi1

  • 1Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Entropy (Basel, Switzerland)
|July 8, 2023
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Summary

We introduce mixture complexity (MC), a continuous measure for cluster size in finite mixture models, accounting for overlaps and weight biases. This new criterion enables earlier detection of gradual clustering changes and analysis of substructures.

Keywords:
change detectionclusteringfinite mixture modelgradual changeinformation theory

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Mining

Background:

  • Finite mixture models are widely used for data clustering.
  • Existing methods often equate cluster size with mixture component count, which is inaccurate with overlapping clusters or biased weights.
  • Interpreting cluster structures requires a more nuanced measure of cluster size.

Purpose of the Study:

  • To propose a novel, continuous measure for cluster size in finite mixture models.
  • To introduce the concept of mixture complexity (MC) for a more accurate representation of cluster structure.
  • To apply MC for detecting gradual changes in clustering over time.

Main Methods:

  • Formulated mixture complexity (MC) from an information-theoretic perspective.
  • Defined MC as a continuous value extending traditional cluster size measures.
  • Applied MC to analyze gradual clustering changes and hierarchical structures.

Main Results:

  • Mixture complexity (MC) accurately measures cluster size, considering overlaps and weight biases.
  • MC allows for earlier detection of gradual clustering changes compared to abrupt change detection.
  • MC can be decomposed hierarchically, facilitating detailed substructure analysis.

Conclusions:

  • Mixture complexity (MC) offers a robust and interpretable measure for cluster size in finite mixture models.
  • MC provides a novel framework for gradual clustering change detection, enhancing analytical capabilities.
  • The hierarchical decomposition of MC aids in understanding complex mixture model structures.