Learning metrics via discriminant kernels and multidimensional scaling: toward expected Euclidean representation
Zhihua Zhang · 2003
Distance-based methods in machine learning and pattern recognition have to rely on a metric distance between points in the input space. Instead of specifying a metric a pri-ori, we seek to learn the metric from data via kernel methods and multidimensional scal-ing (MDS) techniques. Under the classifica-tion setting, we define discriminant kernels on the joint space of input and output spaces and present a specific family of discriminant kernels. This family of discriminant ker-nels is attractive because the induced met-rics are Euclidean and Fisher separable, and MDS techniques can be used to find the low-dimensional Euclidean representations (also called feature vectors) of the induced met-rics. Since the feature vectors incorporate information from both input points and their corresponding labels and they enjoy Fisher separability, they are appropriate to be used in distance-based classifiers. 1.