Spectral Clustering for Medical Imaging

Spectral clustering is often reported in the literature as successfully being applied to applications from image segmentation to community detection. However, what is not reported is that great time and effort are required to construct a graph Laplacian to achieve these successes. This problem which we call Laplacian construction is critical for the success of spectral clustering but is not well studied by the community. Instead the best Laplacian is typically learnt for each domain from trial and error. This is problematic for areas such as medical imaging since: i) the same images can be segmented in multiple ways depending on the application focus and ii) we don't wish to construct one Laplacian, rather we wish to create a method to construct a Laplacian for each patient's scan. In this paper we attempt to automate the process of Laplacian creation with the help of guidance towards the application focus. In most domains creating a basic Laplacian is plausible, so we propose adjusting this given Laplacian by discovering important nodes. We formulate this problem as an integer linear program with a precise geometric interpretation which is globally minimized using large scale solvers such as Gurobi. We show the usefulness on a real world problem in the area of fMRI scan segmentation where methods using standard Laplacians perform poorly.