February Fourier Talks 2017

Graph-based data representation techniques are a staple of brain network analysis. Weighted graphs are constructed from fMRI and/or sMRI data (via correlation of time series from fMRI, or via probabilistic tractography from sMRI), and various quantities derived from these graphs provide mechanisms for exploring the architecure of brain networks of normal and diseased subjects, at both the individual level and groups of subjects. Spectral clustering, which uses eigenvectors of the graph Laplacian matrix to generate a low-dimensional data representation that is amenable to clustering, is a key tool in characterizing both functional and structural network connectivity in the brain. In this talk, we will discuss some recent advances in the underlying data representation techniques upon which spectral clustering is based, and how these advances might be applicable to exploring brain networks. First, robust techniques have been developed for constructing weighted graphs that identify and exploit discriminative features in the data. Second, efficient methods for "biased" spectral clustering have emerged that enable identification of clusters that are correlated with a user-provided subset of graph vertices. Third, methods for injecting attracting or repelling "potentials" into graph-based data representations enable user-guided spectral clustering or manifold alignment. We provide examples of how each of these recent advances can be applied to investigate functional and structural connectivity networks at both the individual and group levels.