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In this paper, we present a novel method for obtaining a low dimensional representation of a complex brain network that: (1) can be interpreted in a neurobiologically meaningful way, (2) emphasizes group differences by accounting for label information, and (3) captures the variation in disease subtypes/severity by respecting the intrinsic manifold structure underlying the data. Our method is a supervised variant of non-negative matrix factorization (NMF), and achieves dimensionality reduction by extracting an orthogonal set of subnetworks that are interpretable, reconstructive of the original data, and also discriminative at the group level. In addition, the method includes a manifold regularizer that encourages the low dimensional representations to be smooth with respect to the intrinsic geometry of the data, allowing subjects with similar disease-severity to share similar network representations. While the method is generalizable to other types of non-negative network data, in this work we have used structural connectomes (SCs) derived from diffusion data to identify the cortical/subcortical connections that have been disrupted in abnormal neurological state. Experiments on a traumatic brain injury (TBI) dataset demonstrate that our method can identify subnetworks that can reliably classify TBI from controls and also reveal insightful connectivity patterns that may be indicative of a biomarker.

Label-Informed Non-negative Matrix Factorization with Manifold Regularization for Discriminative Subnetwork Detection