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Related Experiment Videos

Component retention in principal component analysis with application to cDNA microarray data.

Richard Cangelosi1, Alain Goriely

  • 1Program in Applied Mathematics, University of Arizona, Tucson, AZ85721, USA. rcan@math.arizona.edu

Biology Direct
|January 19, 2007
PubMed
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This study introduces Shannon entropy for estimating interpretable components in principal component analysis. A modified broken stick model incorporating effective degeneracy improves dimension determination for datasets.

Area of Science:

  • Statistics
  • Bioinformatics
  • Data Analysis

Background:

  • Principal Component Analysis (PCA) is a common dimensionality reduction technique.
  • Determining the optimal number of interpretable components in PCA is crucial for accurate data analysis.
  • Existing stopping rules for dimension determination have limitations.

Purpose of the Study:

  • To estimate the number of interpretable components in PCA using Shannon entropy.
  • To review and propose modifications to existing dimension determination methods.
  • To evaluate the performance of these methods on real and simulated data.

Main Methods:

  • Application of Shannon entropy for component estimation.
  • Review of ad hoc stopping rules for PCA.

Related Experiment Videos

  • Development of a modified broken stick model incorporating a test for effective degeneracy.
  • Allocation of total variance among subspaces.

    • Main Results:

    • Shannon entropy provides a viable estimate for interpretable components in PCA.
    • The modified broken stick model, accounting for effective degeneracy, shows improved performance.
    • Comparative analysis demonstrates the effectiveness of the proposed methods on microarray and simulated data.

    Conclusions:

    • Shannon entropy is a valuable tool for PCA dimension determination.
    • The modified broken stick model offers a more robust approach to identifying significant components.
    • The findings contribute to more reliable analysis of high-dimensional datasets.