Joint Learning of Discriminative Prototypes and Large Margin Nearest Neighbor Classifiers

Abstract

In this paper, we raise important issues concerning the evaluation complexity of existing Mahalanobis metric learning methods. The complexity scales linearly with the size of the dataset. This is especially cumbersome on large scale or for real-time applications with limited time budget. To alleviate this problem we propose to represent the dataset by a fixed number of discriminative prototypes. In particular, we introduce a new method that jointly chooses the positioning of prototypes and also optimizes the Mahalanobis distance metric with respect to these. We show that choosing the positioning of the prototypes and learning the metric in parallel leads to a drastically reduced evaluation effort while maintaining the discriminative essence of the original dataset. Moreover, for most problems our method performing k-nearest prototype (k-NP) classification on the condensed dataset leads to even better generalization compared to k-NN classification using all data. Results on a variety of challenging benchmarks demonstrate the power of our method. These include standard machine learning datasets as well as the challenging Public Figures Face Database. On the competitive machine learning benchmarks we are comparable to the state-of-the-art while being more efficient. On the face benchmark we clearly outperform the state-of-the-art in Mahalanobis metric learning with drastically reduced evaluation effort.