Group pattern detection of longitudinal data using functional statistics

TL;DR

This paper introduces a novel approach combining functional analysis of variance and permutation tests to detect group patterns in longitudinal data, effectively identifying significant differences over time with applications in facial emotion analysis.

Contribution

The paper presents a new method that integrates FANOVA and permutation tests for group pattern detection in limited sample size longitudinal data, improving interpretability and accuracy.

Findings

Effective in identifying significant time zones of group differences

Accurate in extracting emotional behaviors from facial data

Validated through simulation and real-world facial emotion dataset

Abstract

Estimations and evaluations of the main patterns of time series data in groups benefit large amounts of applications in various fields. Different from the classical auto-correlation time series analysis and the modern neural networks techniques, in this paper we propose a combination of functional analysis of variance (FANOVA) and permutation tests in a more intuitive manner for a limited sample size. First, FANOVA is applied in order to separate the common information and to dig out the additional categorical influence through paired group comparison, the results of which are secondly analyzed through permutation tests to identify the time zones where the means of the different groups differ significantly. Normalized kernel functions of different groups are able to reflect remarkable mean characteristics in grouped unities, also meaningful for deeper interpretation and group-wise classification. In order to learn whether and when the proposed method of FANOVA and permutation F-test works precisely and efficiently, we compare the estimated kernel results with the ground truth on simulated data. After the confirmation of the model's efficiency from simulation, we apply it also to the RAVDESS facial dataset to extract the emotional behaviors of humans based on facial muscles contractions (so-called action units (AU) technically in computer graphics), by comparing the neutral performances with emotional ones.