Learning Local Invariant Mahalanobis Distances

For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance. Metric learning is a machine learning task which learns a distance metric d(x, y) between data points, based on data instances. As distances play an important role in many machine learning algorithms, e.g.