Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis

2026-07-24

AI Summary

This work addresses the complex inter-individual variability in both spatial and temporal patterns inherent in multi-subject neuroimaging data by proposing a Spatio-Temporal Variational Tensor Decomposition (ST-VTD) framework. The method integrates a tensor generative model with structured priors, jointly modeling shared and subject-specific spatio-temporal structures through an LL1-inspired low-rank spatial regularizer and a learnable LSTM-based temporal prior. Efficient and interpretable parameter estimation is achieved by combining amortized variational inference with a group ICA warm-start strategy. Evaluated on simulated fMRI data, ST-VTD substantially outperforms existing classical and probabilistic decomposition approaches, demonstrating markedly improved accuracy in recovering latent factors.

Abstract

Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects. Existing matrix and tensor decompositions provide interpretable factorizations, but rely on fixed multilinear structures or coupling schemes that may limit their flexibility in capturing complex variability. In this work, we introduce a spatiotemporal variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors to jointly represent spatial maps and temporal dynamics. Spatial factors are regularized to promote a low-rank structure inspired by the LL1 decomposition, while temporal factors are modeled using a learned Long short-term memory (LSTM)-based prior, enabling flexible and adaptive dynamics. Posterior inference is performed using an amortized variational formulation by unrolling iterations of an optimization algorithm, leading to an interpretable and parameter-efficient architecture. The proposed inference framework employs a warm-start strategy based on group independent component analysis, which we found to improve optimization performance. Experiments on a realistic synthetic functional MRI (fMRI) dataset demonstrate that the proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.

Problem

• multisubject spatiotemporal data
• tensor decomposition
• shared and subject-specific structure
• neuroimaging
• variability modeling

Innovation

• variational tensor decomposition
• low-rank structure
• LSTM-based prior
• amortized inference
• spatiotemporal data