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Convex clustering analysis for histogram-valued data.

Cheolwoo Park1, Hosik Choi2, Chris Delcher3

  • 1Department of Statistics, University of Georgia, Athens, Georgia 30602.

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Summary
This summary is machine-generated.

This study introduces a new regularized convex clustering method for histogram-valued data. This approach effectively groups symbolic data, outperforming existing methods in numerical examples.

Keywords:
Wassertein-Kantorovich metricclusteringhistogram-valued dataquantilesregularization

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Area of Science:

  • Statistics
  • Data Science
  • Machine Learning

Background:

  • Symbolic data analysis (SDA) is gaining traction for its ability to handle complex data structures.
  • Traditional statistical methods struggle with symbolic data, necessitating novel analytical techniques.
  • Histogram-valued data, a type of symbolic data, requires specialized grouping methods.

Purpose of the Study:

  • To develop a novel regularized convex clustering approach for grouping histogram-valued data.
  • To adapt convex clustering techniques for the unique challenges posed by symbolic data analysis.
  • To evaluate the performance of the proposed method against existing clustering algorithms.

Main Methods:

  • Developed a regularized convex clustering algorithm tailored for histogram-valued data.
  • Utilized penalization of parameters as a relaxation of hierarchical clustering.
  • Employed two distinct distance metrics to quantify dissimilarity between histogram data.

Main Results:

  • The proposed regularized convex clustering method successfully grouped histogram-valued data.
  • Numerical examples demonstrated superior performance compared to competing methods.
  • The approach effectively leverages the structural information inherent in symbolic data.

Conclusions:

  • The developed regularized convex clustering method is effective for analyzing histogram-valued symbolic data.
  • This technique offers an improvement over traditional statistical approaches for complex data.
  • The findings highlight the potential of convex clustering in symbolic data analysis.