Robust Functional PCA for Relative Data

This article introduces a robust approach to functional principal component analysis (FPCA) for relative data. While recent papers have studied relative functional 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 relative functional data. Based on this extension, we introduce a new method, robust relative principal component analysis (RRPCA), 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.