Geodesic Clustering of Positive Definite Matrices For Classification of Mental Disorder Using Brain Functional Connectivity

Functional Magnetic Resonance Imaging (fMRI) is a commonly used technique to evaluate brain activity, and can be used to distinguish patients from healthy controls in a variety of diseases. In this work, we present a two-step approach to discriminate healthy subjects against those affected by either Autism Spectrum Disorder or Schizophrenia on the basis of their connectivity patterns. We exploited the property that connectivity patterns described by positive definite matrices define a Riemannian manifold. In this framework, to generate a vector representation used in the classification task, we performed a geodesic clustering of the connectivity matrices. Cluster centroids were then used as a dictionary allowing to encode all subjects graphs as vectors of geodesic distances. A linear Support Vector Machine was then used to classify subjects. To show the advantage of using geodesic distances for this problem, the same analysis was conducted using a Euclidean metric. Experiments show that employing Euclidean distances leads to a lower classification performance and possibly to the definition of the wrong number of clusters, whereas geodesic clustering results in a significantly improved accuracy.