Matrix-Variate Regression for Sparse, Low-Rank Estimation of Brain Connectivities Associated With a Clinical Outcome

• Published in: IEEE transactions on biomedical engineering Vol. 71; no. 4; pp. 1378 - 1390
• Main Authors: Brzyski, Damian, Hu, Xixi, Goni, Joaquin, Ances, Beau, Randolph, Timothy W, Harezlak, Jaroslaw
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Arrays; Brain; Brain - diagnostic imaging; Brain - physiology; Brain modeling; Brain network clustering; Clinical outcomes; Cognition; Covariance matrices; Estimation; HIV; Human immunodeficiency virus; Humans; low-rank and sparse matrix; Matrix decomposition; Neural networks; Neuroimaging; nuclear plus L1 norm; penalized matrix regression; Phenotypes; Regression coefficients; Sparse matrices; spectral regularization; Tensors
• ISSN: 0018-9294; 1558-2531; 1558-2531
• DOI: 10.1109/TBME.2023.3336241

Objective: We address the problem of finding brain connectivities that are associated with a clinical outcome or phenotype. Methods: The proposed framework regresses a (scalar) clinical outcome on matrix-variate predictors which arise in the form of brain connectivity matrices. For example, in a large cohort of subjects we estimate those regions of functional connectivities that are associated with neurocognitive scores. We approach this high-dimensional yet highly structured estimation problem by formulating a regularized estimation process that results in a low-rank coefficient matrix having a sparse set of nonzero entries which represent regions of biologically relevant connectivities. In contrast to the recent literature on estimating a sparse, low-rank matrix from a single noisy observation, our scalar-on-matrix regression framework produces a data-driven extraction of structures that are associated with a clinical response. The method, called Sp arsity I nducing N uclear- N orm E stimato r (SpINNEr), simultaneously constrains the regression coefficient matrix in two ways: a nuclear norm penalty encourages low-rank structure while an <inline-formula><tex-math notation="LaTeX">\ell _{1}</tex-math></inline-formula> norm encourages entry-wise sparsity. Results: Our simulations show that SpINNEr outperforms other methods in estimation accuracy when the response-related entries (representing the brain's functional connectivity) are arranged in well-connected communities. SpINNEr is applied to investigate associations between HIV-related outcomes and functional connectivity in the human brain. Conclusion and Significance: Overall, this work demonstrates the potential of SpINNEr to recover sparse and low-rank estimates under scalar-on-matrix regression framework.