Orthonormal pairwise logratio selection (OPALS) algorithm for compositional data analysis in high dimensions

Area of Science:

• Compositional data analysis
• High-dimensional statistics
• Bioinformatics

Background:

• Pairwise logratios are fundamental in compositional data analysis.
• Existing logratio coordinate systems can be computationally intensive for high dimensions.
• A need exists for efficient methods to represent all pairwise logratios.

Purpose of the Study:

• To present an efficient algorithm (OPALS) for obtaining orthonormal pairwise logratios.
• To alleviate the computational burden of high-dimensional compositional data analysis.
• To explore the relationship between orthonormal pairwise logratios and pivot coordinates in regression and classification.

Main Methods:

• Development of the OPALS algorithm based on Latin squares theory.
• Efficient computation of orthonormal pairwise logratios from D-1 logratio systems.
• Application and illustration using contemporary molecular biology data.

Main Results:

• OPALS enables efficient computation of all orthonormal pairwise logratios.
• The algorithm significantly reduces computational complexity for high-dimensional data.
• Demonstrated feasibility and properties of the method through real-world examples.

Conclusions:

• The OPALS algorithm provides a computationally feasible approach for high-dimensional compositional data analysis.
• This method enhances the utility of fine-grained logratio representations.
• The findings are relevant for statistical modeling and analysis in fields like molecular biology.