Algorithmic Geometry Shapes the Biological Meaning of Thalamocortical Structural Covariance

Neuroimaging studies often derive and discuss structural covariance (SC) as a representation of underlying brain circuitry that reflects coordinated maturation, anatomical connectivity, transcriptional similarity, and shared genetic influences. These associations motivate its use to study brain organization across development, aging, and disease. However, the algorithms used to derive SC networks impose constraints that may shape their biological interpretation. To understand the impact of algorithm choice, we used the thalamocortical system as an example and compared five common representations of voxelwise SC, namely, principal component analysis (PCA), independent component analysis (ICA), non-negative matrix factorization (NMF), orthogonal projective NMF (OPNMF), and \textit{k}-means clustering, in 755 participants aged 8--22 years from the Philadelphia Neurodevelopmental Cohort (PNC). SC networks derived from deformation-based morphometry (DBM) were evaluated against three complementary biological benchmarks: age-related individual differences, fractional-anisotropy (FA)-based microstructural connectivity of regionally-specific thalamocortical connections, and Allen Human Brain Atlas gene expression. Each algorithm demonstrated underlying sensitivity to differing aspects of neurobiology: PCA and OPNMF showed the strongest associations between participant-level component weights and age. NMF, OPNMF, and \textit{k}-means showed greater spatial overlap between positive cortical SC and tractography-derived projections. ICA and PCA showed stronger correspondence between thalamic and cortical gene-expression profiles across the transcriptome, whereas NMF, OPNMF, and \textit{k}-means more often identified thalamic components with relatively high core-matrix gene expression. This study emphasizes that algorithmic constraints effectively act as biological priors and decomposition methods do not provide neutral compression of the data. We conclude that it is critical to consider whether the algorithmic objective matches the representational geometry of the neurobiology being studied. Overall, our findings suggest that SC studies should select and justify algorithms according to the biological question, explicitly considering whether their constraints favour distributed gradients, overlapping regional parts, or discrete clusters. Meanwhile, interpretations of SC findings could also be informed by the specific algorithmic constraints used to derive them.