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We present a method for metric optimization in the Large DeformationDiffeomorphic Metric Mapping (LDDMM) framework, by treating the inducedRiemannian metric on the space of diffeomorphisms as a kernel in a machinelearning context. For simplicity, we choose the kernel Fischer LinearDiscriminant Analysis (KLDA) as the framework. Optimizing the kernel parametersin an Expectation-Maximization framework, we define model fidelity via thehinge loss of the decision function. The resulting algorithm optimizes theparameters of the LDDMM norm-inducing differential operator as a solution to agroup-wise registration and classification problem. In practice, this may leadto a biology-aware registration, focusing its attention on the predictive taskat hand such as identifying the effects of disease. We first tested ouralgorithm on a synthetic dataset, showing that our parameter selection improvesregistration quality and classification accuracy. We then tested the algorithmon 3D subcortical shapes from the Schizophrenia cohort Schizconnect. OurSchizpohrenia-Control predictive model showed significant improvement in ROCAUC compared to baseline parameters.

Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphisms