A Novel Distance-based Classifier Using Convolution Kernels and Euclidean Embeddings

Distance-based classification methods such as the nearest-neighbor and k-nearest-neighbor classifiers have to rely on a metric or distance measure between points in the input space. For many applications, Euclidean distance in the input space is not a good choice and hence more complicated distance measures have to be used. In this paper, we propose a novel kernel-based method that achieves Euclidean embedding by ensuring that the feature space is always Euclidean. Thus, Euclidean distance-based classification methods can be applied in the feature space. Unlike typical kernels which correspond to a nonlinear mapping from the input space, our kernel function corresponds to a nonlinear mapping from the joint space incorporating both the input and class label spaces. The kernel function, which can be seen as a convolution kernel formed from the tensor product kernel and the direct sum kernel, tends to increase the separability between classes. We have applied our new classification method to some face recognition benchmark datasets. Our method is significantly faster than other face recognition methods and yet it can deliver comparable classification accuracy.