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Estimating the number of principal components via Split-Half Eigenvector Matching (SHEM).

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Methodsx
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PubMed
Summary

This study introduces a new method for estimating the number of principal components in dimension reduction. By comparing data splits, it offers a more accurate way to determine the true number of independent components.

Keywords:
Dimension reductionEigenvectorsNumber of componentsPrincipal component analysisSHEM: Split-Half Eigenvector Matching

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Area of Science:

  • Statistics
  • Data Science
  • Machine Learning

Background:

  • Principal Component Analysis (PCA) is crucial for dimension reduction.
  • Existing methods for selecting the number of principal components may be suboptimal.
  • Accurate component selection is vital for reliable data analysis.

Purpose of the Study:

  • To present an alternative procedure for estimating the optimal number of principal components.
  • To recover the true number of independent vectors underlying data generation.
  • To validate a novel approach using data splitting and similarity analysis.

Main Methods:

  • Repeatedly splitting data into random halves.
  • Comparing eigenvectors derived from each data half.
  • Analyzing the split between high and low similarity scores to estimate component count.

Main Results:

  • The proposed method demonstrates a proof of principle for estimating principal components.
  • Similarity analysis across data splits provides a useful estimation approach.
  • The technique is applicable to dimension reduction and similar modeling problems.

Conclusions:

  • Data splitting and similarity comparison offer a viable strategy for determining the number of principal components.
  • This method enhances the accuracy of dimension reduction techniques.
  • The approach holds promise for improving various statistical modeling applications.