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Robust principal component analysis for compositional tables.

J de Sousa1, K Hron1, K Fačevicová1

  • 1Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Olomouc, Czech Republic.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces a new coordinate system for analyzing compositional tables, simplifying the interpretation of relationships between factors like age and gender in unemployment data. This method enhances robust principal component analysis (rPCA) for better data exploration.

Keywords:
Compositional datacompositional tableindependence tableinteraction tablepivot coordinatesrobust principal component analysis

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Area of Science:

  • Statistics
  • Data Analysis
  • Multivariate Analysis

Background:

  • Data tables with multiple factors can be viewed as compositional data.
  • Analyzing multiple compositional tables jointly, especially with varying scales, presents challenges.
  • Existing logratio methods offer orthonormal coordinates but lack direct interpretability and ease of exploration.

Purpose of the Study:

  • To propose a novel coordinate system for compositional tables.
  • To facilitate the interpretation of relationships between factors within tables.
  • To enable the application of robust principal component analysis (rPCA) to compositional data.

Main Methods:

  • Developing a special choice of coordinates directly related to centered logratio (clr) coefficients.
  • Applying robust principal component analysis (rPCA) for dimension reduction.
  • Linking orthonormal coordinates with clr coefficients to overcome singularity issues.

Main Results:

  • The proposed coordinates offer direct interpretability in terms of original table cells.
  • This approach allows for effective dimension reduction and exploration of factor relationships.
  • The method successfully integrates rPCA with compositional data analysis.

Conclusions:

  • The new coordinate system simplifies the analysis of compositional tables.
  • This method enhances the exploration of relationships between factors in multivariate data.
  • The approach provides a robust and interpretable framework for compositional data analysis using rPCA.