  In this paper, we propose a nonlinear distance metric learning scheme based
on the fusion of component linear metrics. Instead of merging displacements at
each data point, our model calculates the velocities induced by the component
transformations, via a geodesic interpolation on a Lie transfor- mation group.
Such velocities are later summed up to produce a global transformation that is
guaranteed to be diffeomorphic. Consequently, pair-wise distances computed this
way conform to a smooth and spatially varying metric, which can greatly benefit
k-NN classification. Experiments on synthetic and real datasets demonstrate the
effectiveness of our model.
