On optimal allocation of treatment/condition variance in principal component analysis

TL;DR

This paper investigates how the pattern and magnitude of loadings across conditions affect the optimal allocation of variance in principal component analysis, with implications for various research domains.

Contribution

It identifies that similar loading patterns across conditions are necessary for optimal variance allocation in PCA, expanding understanding beyond loading magnitudes.

Findings

Similar loading patterns across conditions are necessary for optimal variance allocation.

Loading magnitude similarity is not necessary for optimal allocation.

The study broadens PCA application insights in multiple research fields.

Abstract

The allocation of a (treatment) condition-effect on the wrong principal component (misallocation of variance) in principal component analysis (PCA) has been addressed in research on event-related potentials of the electroencephalogram. However, the correct allocation of condition-effects on PCA components might be relevant in several domains of research. The present paper investigates whether different loading patterns at each condition-level are a basis for an optimal allocation of between-condition variance on principal components. It turns out that a similar loading shape at each condition-level is a necessary condition for an optimal allocation of between-condition variance, whereas a similar loading magnitude is not necessary.