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 Sparsity Inducing Nuclear-Norm Estimator (SpINNEr), simultaneously constrains the regression coefficient matrix in two ways: a nuclear norm penalty encourages low-rank structure while anℓ1 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.

Original languageEnglish
Pages (from-to)1378-1390
Number of pages13
JournalIEEE Transactions on Biomedical Engineering
Issue number4
StatePublished - Apr 1 2024


  • Brain network clustering
  • low-rank and sparse matrix
  • nuclear plus L1 norm
  • penalized matrix regression
  • spectral regularization


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