Latent Functional PARAFAC for modeling multidimensional longitudinal data

TL;DR

This paper introduces a probabilistic tensor decomposition method for modeling high-dimensional longitudinal data with smooth functional structures, enabling efficient analysis of sparse and irregularly sampled datasets.

Contribution

It proposes a novel latent functional PARAFAC model with a probabilistic framework and a covariance-based algorithm, advancing tensor analysis for longitudinal data.

Findings

Effective in reconstructing tensors in simulations

Applicable to sparse and irregular sampling schemes

Successfully applied to neurocognitive data in ADNI study

Abstract

In numerous settings, it is increasingly common to deal with longitudinal data organized as high-dimensional multi-dimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often implies a smooth functional structure on one of the tensor modes. To help researchers investigate such data, we introduce a new tensor decomposition approach based on the CANDECOMP/PARAFAC decomposition. Our approach allows for representing a high-dimensional functional tensor as a low-dimensional set of functions and feature matrices. Furthermore, to capture the underlying randomness of the statistical setting more efficiently, we introduce a probabilistic latent model in the decomposition. A covariance-based block-relaxation algorithm is derived to obtain estimates of model parameters. Thanks to the covariance formulation of the solving procedure and thanks to the probabilistic modeling, the method can be used in sparse and irregular sampling schemes, making it applicable in numerous settings. We apply our approach to help characterize multiple neurocognitive scores observed over time in the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. Finally, intensive simulations show a notable advantage of our method in reconstructing tensors.