Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis
Authors: Laura M. Montaldo, Ricardo A. Borsoi, Sebastian Miron, Tulay Adali
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.
Accelerated acquisition of fMRI enables enhanced detection of neurovascular (BOLD) activity in the brain, but image reconstruction becomes challenging with high k-space undersampling: Task-evoked BOLD signals are small in magnitude, which traditional anatomical MRI reconstruction methods fail to recover, as they favor spatial accuracy over temporal fidelity. We present DD-INR, a Dynamics-Driven Implicit Neural Representation framework tailored for accelerated fMRI that benefits from incoherent time-varying sampling and a tailored spatiotemporal prior, outperforming traditional methods, demonstrated in simulation and in-vivo acquisition, both in terms of image quality and retrieval of activation patterns. DD-INR achieves this by splitting the fMRI data into a static background and a temporally varying dynamic component, representing only the dynamics with a dedicated INR, thereby focusing the model's capacity on activation-relevant changes while remaining compact. In general, DD-INR provides a promising framework for accelerated fMRI reconstruction, with the potential to improve the sensitivity and robustness of fMRI studies within practical scan time limits. The source code is available at https://github.com/JoosenLi/DD-INR.
We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.
Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.