A tensor based varying-coefficient model for multi-modal neuroimaging data analysis

• Published in: IEEE transactions on signal processing Vol. 72; pp. 1 - 13
• Main Authors: Niyogi, Pratim Guha, Lindquist, Martin A., Maiti, Tapabrata
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: B spline functions; B-spline; Basis functions; Brain modeling; CP decomposition; Data analysis; Data models; Data structures; Electroencephalography; Eye movements; Functional linear model; Functional magnetic resonance imaging; Functional MRI; Imaging; Magnetic resonance imaging; Medical imaging; Multi-modal analysis; Neuroimaging; Regression coefficients; Regression models; Tensors; Multi-modal analysis; Functional MRI; B-spline; CP decomposition; Functional linear model
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2024.3375768

All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time neuroimaging data is increasingly being combined with other non-imaging modalities, such as behavioral and genetic data. The data structure of many of these modalities can be expressed as time-varying multidimensional arrays (tensors), collected at different time-points on multiple subjects. Here, we consider a new approach for the study of neural correlates in the presence of tensor-valued brain images and tensor-valued covariates, where both data types are collected over the same set of time points. We propose a time-varying tensor regression model with an inherent structural composition of responses and covariates. Regression coefficients are expressed using the B-spline technique, and the basis function coefficients are estimated using CP-decomposition by minimizing a penalized loss function. We develop a varying-coefficient model for the tensor-valued regression model, where both covariates and responses are modeled as tensors. This development is a non-trivial extension of function-on-function concurrent linear models for complex and large structural data, where the inherent structures are preserved. In addition to the methodological and theoretical development, the efficacy of the proposed method based on both simulated and real data analysis (e.g., the combination of eye-tracking data and functional magnetic resonance imaging (fMRI) data) is also discussed.