Identifying Important Pairwise Logratios in Compositional Data with Sparse Principal Component Analysis

Area of Science:

• Statistics
• Chemometrics
• Data Science

Background:

• Compositional data analysis relies on pairwise logratios, which can become unmanageable in high-dimensional datasets.
• Interpreting a large number of pairwise logratios in multivariate analysis poses significant challenges.

Purpose of the Study:

• To develop a sparse method for identifying essential pairwise logratios in compositional data.
• To improve the interpretability of multivariate analyses for compositional datasets.

Main Methods:

• Construction of all possible pairwise logratios from compositional data.
• Application of sparse principal component analysis (SPCA) to select important logratios.
• Development of three visual tools for model interpretation.

Main Results:

• The proposed sparse method effectively identifies a subset of important pairwise logratios.
• Simulated and real-world data demonstrated the procedure's performance.
• Visual tools aid in understanding the trade-off between sparsity and explained variability, logratio stability, and part importance.

Conclusions:

• Sparse methods offer a viable solution for managing complexity in compositional data analysis.
• The proposed SPCA-based procedure and visualization tools enhance the practical interpretability of compositional data models.