Structural propagation barely moves brain-connectome classification: dropping it leaves accuracy near 0.65
Synopsis
Multimodal brain-connectome analysis usually treats structural connectivity as a propagation channel and functional connectivity as the signal carried through it. A Wasserstein Weisfeiler-Lehman kernel instead represents each subject as one weighted graph with continuous node attributes and compares subjects by optimal transport between point clouds. On a 900-subject synthetic cohort it reaches 0.651±0.028 balanced accuracy, significantly above a raw-feature SVM and a histogram WL kernel, yet replacing the propagation operator with the identity leaves performance essentially unchanged, so the discriminative gain comes mainly from the Wasserstein representation of functional attributes.
Interpretation
Multimodal connectome information can now be compared inside a single graph without first constructing external coupling weights between a structural layer and a functional layer. Earlier multilayer-network approaches kept structural and functional connectomes as separate layers, with their interaction mediated by an additional set of interlayer weights estimated outside either layer. On a 900-subject synthetic cohort with three ordered CN/MCI/AD groups, the kernel reaches 0.651±0.028 balanced accuracy under nested cross-validation, significantly outperforming a raw-feature SVM and a histogram-based WL-kernel baseline.
Each subject becomes one weighted graph: diffusion-tractography streamlines supply the weighted edges, and resting-state functional-connectivity correlation profiles become continuous attributes on each brain region. Weisfeiler-Lehman-style propagation repeatedly averages each region's attribute over its structural neighbourhood, re-expressing the functional profile in its anatomical surroundings hop by hop. Features from successive hops are concatenated into a point cloud, subjects are compared with an L1-Wasserstein distance under a Euclidean ground metric, and an exponential kernel yields the kernel matrix; exact W1 costs about 1.6 ms per pair on a 100-region parcellation.
The discriminative gain is associated mainly with the Wasserstein point-cloud representation rather than with structural propagation. Replacing the propagation operator by the identity, which removes structural propagation entirely, leaves classification performance essentially the same as local and fractional WWL, whereas a structure-only control stays near chance. The identity-propagation control scores 0.653±0.029 balanced accuracy, local WWL 0.651±0.028, fractional WWL 0.654±0.028, and the structure-only control 0.316±0.023 against a chance level of 0.333.
Perspective
The conclusions rest on controlled synthetic cohorts: 900 subjects generated from six independently seeded structural templates, a functional signal defined as a progressive age-dependent loss of resting-state network segregation, and clinical variables produced by the generative model. The authors propose next constructing functional perturbations with controlled spatial support, for example concentrating the network-segregation signal within selected resting-state networks, to test directly whether signal spatial scale predicts the relative behaviour of local and fractional propagation.
The authors state that the interpretation, non-local propagation helping diffuse whole-brain signals while weakening correspondence for network-segregation signals, is a hypothesis suggested by the controlled benchmarks rather than a demonstrated general property; the biomarker associations partly follow from how the synthetic cohort was generated and should be read as a demonstration of the readout the representation offers, not as clinical validity. All experiments use synthetic cohorts, and the authors require validation on independent empirical neuroimaging data before judging whether these behaviours extend.