  In recent years, research efforts to extend linear metric learning models to
handle nonlinear structures have attracted great interests. In this paper, we
propose a novel nonlinear solution through the utilization of deformable
geometric models to learn spatially varying metrics, and apply the strategy to
boost the performance of both kNN and SVM classifiers. Thin-plate splines (TPS)
are chosen as the geometric model due to their remarkable versatility and
representation power in accounting for high-order deformations. By transforming
the input space through TPS, we can pull same-class neighbors closer while
pushing different-class points farther away in kNN, as well as make the input
data points more linearly separable in SVMs. Improvements in the performance of
kNN classification are demonstrated through experiments on synthetic and real
world datasets, with comparisons made with several state-of-the-art metric
learning solutions. Our SVM-based models also achieve significant improvements
over traditional linear and kernel SVMs with the same datasets.
