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Testing for group structure in high-dimensional data.

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Determining the optimal number of clusters in high-dimensional data using finite mixture models is challenging. This study evaluates a resampling method, assessing potential bias from dimension reduction in clustering analysis.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Mining

Background:

  • Finite mixture models are used for data clustering.
  • Determining the correct number of clusters is a critical challenge.
  • High-dimensional data (p >> n) presents unique difficulties for model fitting.

Purpose of the Study:

  • To investigate the performance of a resampling approach for determining the number of components in mixture models.
  • To assess the impact of dimension reduction on this resampling method in high-dimensional settings.

Main Methods:

  • Utilizing finite mixture models for clustering.
  • Applying a resampling (bootstrapping) approach to test for the number of components.
  • Performing dimension reduction techniques to handle high-dimensional data.
  • Comparing results from bootstrapping on reduced data versus full data.

Main Results:

  • The study examines the potential for bias when bootstrapping is performed only on dimension-reduced data.
  • Performance evaluation of the resampling approach in the context of high-dimensional data.

Conclusions:

  • Dimension reduction is necessary for fitting normal mixture models to high-dimensional data.
  • The research questions the practical significance of bias introduced by performing bootstrapping solely on reduced data.