# Primal path algorithm for compositional data analysis

## TL;DR

This paper introduces an efficient solution path algorithm for $l_1$ regularized regression and classification models tailored for compositional data, addressing computational challenges in high-dimensional settings.

## Contribution

It develops a novel, faster algorithm for compositional data analysis that handles linear constraints more efficiently than existing methods.

## Key findings

- Algorithm significantly reduces computation time.
- Effective in high-dimensional microbiome data analysis.
- Extended to classification tasks with compositional predictors.

## Abstract

Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional computational time, which becomes severe in high-dimensional cases. As such, we propose an efficient solution path algorithm for a $l_1$ regularized regression with compositional data. The algorithm is then extended to a classification model with compositional predictors. We also compare its computational speed with that of previously developed algorithms and apply the proposed algorithm to analyze human gut microbiome data.