Functional factor analysis for periodic remote sensing data

TL;DR

This paper introduces a novel factor rotation method for functional data, specifically designed for periodic remote sensing data, enhancing interpretability and stability in complex covariance scenarios.

Contribution

It proposes a new rotation technique based on canonical correlations toward periodic functions, improving interpretability and computational efficiency for functional principal components.

Findings

Provides stable, interpretable results in complex covariance settings

Demonstrates effectiveness on remote sensing vegetation data

Enhances decomposition into nearly-periodic and aperiodic components

Abstract

We present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components that are nearly-periodic and nearly-aperiodic with a predefined period. We show that the factor rotation can be obtained by calculation of canonical correlations between appropriate spaces which make the methodology computationally efficient. Moreover, we demonstrate that our proposed rotations provide stable and interpretable results in the presence of highly complex covariance. This work is motivated by the goal of finding interpretable sources of variability in gridded time series of vegetation index measurements obtained from remote sensing, and we demonstrate our methodology through an application of factor rotation of this data.