A0480
Title: Functional PARAFAC with probabilistic modeling
Authors: Lucas Sort - CentraleSupelec (France) [presenting]
Laurent Le Brusquet - CentraleSupelec (France)
Arthur Tenenhaus - CentraleSupelec (France)
Abstract: In longitudinal studies, data can increasingly be organized as tensors. Within this framework, the time-continuous property often implies a smooth functional structure on one of the tensor dimensions. To help researchers investigate such data, a new tensor decomposition approach is introduced based on the CANDECOMP/PARAFAC decomposition. The approach allows for the representation of a high-dimensional functional tensor as a low-dimensional set of functions and feature matrices. Furthermore, to capture the underlying randomness of the sampling setting more efficiently, a probabilistic model is introduced in the decomposition. A block-relaxation algorithm using only covariance and cross-covariance operators is derived to obtain estimates of model parameters. Thanks to the covariance formulation of the solving procedure and the probabilistic modeling, the method can be used in sparse and irregular sampling schemes, making it applicable in numerous settings. Intensive simulations are introduced to show the notable advantage of the method in reconstructing tensors and retrieving insightful latent information.
