Riemannian geometry of functional connectivity matrices for multi-site attention-deficit/hyperactivity disorder data harmonization

The use of multi-site datasets in neuroimaging provides neuroscientists with more statistical power to perform their analyses. However, it has been shown that imaging-site introduces a variability in the data that cannot be attributed to biological sources. In this work, we show that functional connectivity matrices derived from resting-state multi-site data contain a significant imaging-site bias. To this aim, we exploited the fact that functional connectivity matrices belong to the manifold of symmetric positive-definite matrices, making possible to operate on them with Riemannian geometry. We hereby propose a geometry-aware harmonization approach, Rigid Log-Euclidean Translation, that accounts for this site bias. Moreover, we adapted other Riemannian-geometric methods designed for other domain adaptation tasks, and compared them to our proposal. Based on our results, Rigid Log-Euclidean Translation of multi-site functional connectivity matrices seems to be among the studied methods the most suitable one in a clinical setting. This represents an advance with respect to previous functional connectivity data harmonization approaches, which do not respect the geometric constraints imposed by the underlying structure of the manifold. In particular, when applying our proposed method on data from the ADHD-200 dataset, a multi-site dataset built for the study of attention-deficit/hyperactivity disorder, we obtained results that display a remarkable correlation with established pathophysiological findings and, therefore, represent a substantial improvement when compared to the non-harmonization analysis. Thus, we present evidence supporting that harmonization should be extended to other functional neuroimaging datasets, and provide a simple geometric method to address it.