Robust functional PCA for relative data

TL;DR

This paper develops a robust functional PCA method for density data within Bayes spaces, effectively handling outliers and noise, and demonstrating improved covariance estimation through simulations and real data.

Contribution

It extends Mahalanobis distance to Bayes spaces and introduces RDPCA, a novel robust FPCA method for density functions with outlier resistance.

Findings

RDPCA outperforms traditional FPCA in noisy conditions

Improves covariance estimation accuracy

Effective on real-world density data

Abstract

This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been limited focus on developing robust methods to effectively handle anomalous observations and large noise. To address this, we extend the Mahalanobis distance concept to Bayes spaces, proposing its regularized version that accounts for the constraints inherent in density data. Based on this extension, we introduce a new method, robust density principal component analysis (RDPCA), for more accurate estimation of functional principal components in the presence of outliers. The method's performance is validated through simulations and real-world applications, showing its ability to improve covariance estimation and principal component analysis compared to traditional methods.