Kernel machine tests of association using extrinsic and intrinsic cluster evaluation metrics

Modeling the network topology of the human brain within the mesoscale has become an increasing focus within the neuroscientific community due to its variation across diverse cognitive processes, in the presence of neuropsychiatric disease or injury, and over the lifespan. Much research has been done on the creation of algorithms to detect these mesoscopic structures, called communities or modules, but less has been done to conduct inference on these structures. The literature on analysis of these community detection algorithms has focused on comparing them within the same subject. These approaches, however, either do not accomodate a more general association between community structure and an outcome or cannot accommodate additional covariates that may confound the association of interest. We propose a semiparametric kernel machine regression model for either a continuous or binary outcome, where covariate effects are modeled parametrically and brain connectivity measures are measured nonparametrically. By incorporating notions of similarity between network community structures into a kernel distance function, the high-dimensional feature space of brain networks, defined on input pairs, can be generalized to non-linear spaces, allowing for a wider class of distance-based algorithms. We evaluate our proposed methodology on both simulated and real datasets.