Diffeomorphic Metric Learning and Template Optimization for Registration-Based Predictive Models

Abstract

We present a method for metric optimization and template construction in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. The construction treats the Riemannian metric on the space of diffeomorphisms as a data-embedding kernel in the context of predictive modeling, here Kernel Logistic Regression (KLR). The task is then to optimize kernel parameters, including the LDDMM metric parameters as well as the registration template, resulting in a parameterized argminimum optimization. In practice, this leads to a group-wise registration problem with the goal of improving predictive performance, for example by focusing the metric and template on discriminating patient and control populations. We validate our algorithm using two discriminative problems on a synthetic data set as well as 3D subcortical shapes from the SchizConnect cohort. Though secondary to the template and kernel optimization, accuracy of schizophrenia classification is improved by LDDMM-KLR compared to linear and RBF-KLR.