Dimensionality reduction techniques in pupillometry research: A primer for behavioral scientists

The measurement of pupil size is a classic tool in psychophysiology, but its popularity has recently surged due to the rapid developments of the eye-tracking industry. Concurrently, several authors have outlined a wealth of strategies for tackling pupillary recordings analytically. The consensus is that the "temporal" aspect of changes in pupil size is key, and that the analytical approach should be mindful of the temporal factor. Here we take a more radical stance on the matter by suggesting that, by the time significant changes in pupil size are detected, it is already too late. We suggest that these changes are indeed the result of distinct, core physiological processes that originate several hundreds of milliseconds before that moment and altogether shape the observed signal. These processes can be recovered indirectly by leveraging dimensionality reduction techniques. Here we therefore outline key concepts of temporal principal components analysis and related rotations to show that they reveal a latent, low-dimensional space that represents these processes very efficiently: a pupillary manifold. We elaborate on why assessing the pupillary manifold provides an alternative, appealing analytical solution for data analysis. In particular, dimensionality reduction returns scores that are (1) mindful of the relevant physiology underlying the observed changes in pupil size, (2) extremely handy and manageable for statistical modelling, and (3) devoid of several arbitrary choices. We elaborate on these points in the form of a tutorial paper for the functions provided in the accompanying R library "Pupilla."