Nearest neighbor classifier generalization through spatially constrained filters

It is widely understood that the performance of the nearest neighbor (NN) rule is dependent on: (i) the way distances are computed between di↵erent examples, and (ii) the type of feature representation used. Linear filters are often used in computer vision as a pre-processing step, to extract useful feature representations. In this paper we demonstrate an equivalence between (i) and (ii) for NN tasks involving weighted Euclidean distances. Specifically, we demonstrate how the application of a bank of linear filters can be re-interpreted, in the form of a symmetric weighting matrix, as a manipulation of how distances are computed between di↵erent examples for NN classification. Further, we argue that filters fulfill the role of encoding local spatial constraints into this weighting matrix. We then demonstrate how these constraints can dramatically increase the generalization capability of canonical distance metric learning techniques in the presence of unseen illumination and viewpoint change.