Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents bounded-distortion metric learning (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a bounded-distortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudo-metric learning and devise the semidefinite relaxation and a randomized algorithm to approximately solve it. We further provide theoretical analysis to show that distortion is a key ingredient for stability and generalization ability of our BDML algorithm. Extensive experiments on several benchmark datasets yield promising results.
Metric learning algorithms can be categorized according to different criteria, such as Mahalanobis @cite_21 @cite_10 @cite_20 and non-Mahalanobis @cite_36 @cite_40 @cite_38 methods; probabilistic @cite_39 @cite_5 and non-probabilistic @cite_23 @cite_37 methods; unsupervised @cite_6 , supervised @cite_41 and semi-supervised @cite_21 methods; and global @cite_17 and local @cite_35 methods.
@cite_38 @cite_37 @cite_35 @cite_36 @cite_41 @cite_21 @cite_6 @cite_39 @cite_40 @cite_23 @cite_5 @cite_10 @cite_20 @cite_17
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We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive formulations for global, multi-task and local metric learning. The resulting algorithms have several advantages over existing methods in the literature: a much smaller number of parameters to be estimated and a principled way to generalize learned metrics to new testing data points. To analyze the approach theoretically, we derive a generalization bound that justifies the sparse combination. Empirically, we evaluate our algorithms on several datasets against state-of-the-art metric learning methods. The results are consistent with our theoretical findings and demonstrate the superiority of our approach in terms of classification performance and scalability. Metric learning aims at finding a distance that approximates a task-specific notion of semantic similarity. Typically, a Mahalanobis distance is learned from pairs of data labeled as being semantically similar or not. In this paper, we learn such metrics in a weakly supervised setting where "bags" of instances are labeled with "bags" of labels. We formulate the problem as a multiple instance learning (MIL) problem over pairs of bags. If two bags share at least one label, we label the pair positive, and negative otherwise. We propose to learn a metric using those labeled pairs of bags, leading to MildML, for multiple instance logistic discriminant metric learning. MildML iterates between updates of the metric and selection of putative positive pairs of examples from positive pairs of bags. To evaluate our approach, we introduce a large and challenging data set, Labeled Yahoo! News, which we have manually annotated and contains 31147 detected faces of 5873 different people in 20071 images. We group the faces detected in an image into a bag, and group the names detected in the caption into a corresponding set of labels. When the labels come from manual annotation, we find that MildML using the bag-level annotation performs as well as fully supervised metric learning using instance-level annotation. We also consider performance in the case of automatically extracted labels for the bags, where some of the bag labels do not correspond to any example in the bag. In this case MildML works substantially better than relying on noisy instance-level annotations derived from the bag-level annotation by resolving face-name associations in images with their captions. Metric learning makes it plausible to learn semantically meaningful distances for complex distributions of data using label or pairwise constraint information. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well. Those that learn multiple metrics throughout the feature space have demonstrated superior accuracy, but at a severe cost to computational efficiency. Here, we adopt a new angle on the metric learning problem and learn a single metric that is able to implicitly adapt its distance function throughout the feature space. This metric adaptation is accomplished by using a random forest-based classifier to underpin the distance function and incorporate both absolute pairwise position and standard relative position into the representation. We have implemented and tested our method against state of the art global and multi-metric methods on a variety of data sets. Overall, the proposed method outperforms both types of method in terms of accuracy (consistently ranked first) and is an order of magnitude faster than state of the art multi-metric methods (16x faster in the worst case). We are interested in supervised metric learning of Mahalanobis like distances. Existing approaches mainly focus on learning a new distance using similarity and dissimilarity constraints between examples. In this paper, instead of bringing closer examples of the same class and pushing far away examples of different classes we propose to move the examples with respect to virtual points. Hence, each example is brought closer to a a priori defined virtual point reducing the number of constraints to satisfy. We show that our approach admits a closed form solution which can be kernelized. We provide a theoretical analysis showing the consistency of the approach and establishing some links with other classical metric learning methods. Furthermore we propose an efficient solution to the difficult problem of selecting virtual points based in part on recent works in optimal transport. Lastly, we evaluate our approach on several state of the art datasets.