text: 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.
  @cite_11: We consider the problem of learning a local metric in order to enhance the performance of nearest neighbor classification. Conventional metric learning methods attempt to separate data distributions in a purely discriminative manner; here we show how to take advantage of information from parametric generative models. We focus on the bias in the information-theoretic error arising from finite sampling effects, and find an appropriate local metric that maximally reduces the bias based upon knowledge from generative models. As a byproduct, the asymptotic theoretical analysis in this work relates metric learning to dimensionality reduction from a novel perspective, which was not understood from previous discriminative approaches. Empirical experiments show that this learned local metric enhances the discriminative nearest neighbor performance on various datasets using simple class conditional generative models such as a Gaussian.
  @cite_2: This paper proposes a conceptually simple but surprisingly powerful method which combines the effectiveness of a discriminative object detector with the explicit correspondence offered by a nearest-neighbor approach. The method is based on training a separate linear SVM classifier for every exemplar in the training set. Each of these Exemplar-SVMs is thus defined by a single positive instance and millions of negatives. While each detector is quite specific to its exemplar, we empirically observe that an ensemble of such Exemplar-SVMs offers surprisingly good generalization. Our performance on the PASCAL VOC detection task is on par with the much more complex latent part-based model of , at only a modest computational cost increase. But the central benefit of our approach is that it creates an explicit association between each detection and a single training exemplar. Because most detections show good alignment to their associated exemplar, it is possible to transfer any available exemplar meta-data (segmentation, geometric structure, 3D model, etc.) directly onto the detections, which can then be used as part of overall scene understanding.
summary: The exemplar-SVM algorithm @cite_2 can be seen as a local similarity measure. This is obtained by maximizing margins, with a linear model, and is weakly supervised as our work. Unlike exemplar-SVM, we learn a Mahalanobis matrix and can learn an invariant metric. Another related work is PMLM @cite_11 , which also finds a local Mahalanobis metric for each data point. However, this method uses global constraints, and therefore cannot work with weakly supervised data, i.e. a single positive example. All the techniques above do not learn local invariant metrics.