  We present a method for metric optimization in the Large Deformation
Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced
Riemannian metric on the space of diffeomorphisms as a kernel in a machine
learning context. For simplicity, we choose the kernel Fischer Linear
Discriminant Analysis (KLDA) as the framework. Optimizing the kernel parameters
in an Expectation-Maximization framework, we define model fidelity via the
hinge loss of the decision function. The resulting algorithm optimizes the
parameters of the LDDMM norm-inducing differential operator as a solution to a
group-wise registration and classification problem. In practice, this may lead
to a biology-aware registration, focusing its attention on the predictive task
at hand such as identifying the effects of disease. We first tested our
algorithm on a synthetic dataset, showing that our parameter selection improves
registration quality and classification accuracy. We then tested the algorithm
on 3D subcortical shapes from the Schizophrenia cohort Schizconnect. Our
Schizpohrenia-Control predictive model showed significant improvement in ROC
AUC compared to baseline parameters.
