This work focuses on active learning of distance metrics from relative comparison information. A relative comparison specifies, for a data point triplet @math , that instance @math is more similar to @math than to @math . Such constraints, when available, have been shown to be useful toward defining appropriate distance metrics. In real-world applications, acquiring constraints often require considerable human effort. This motivates us to study how to select and query the most useful relative comparisons to achieve effective metric learning with minimum user effort. Given an underlying class concept that is employed by the user to provide such constraints, we present an information-theoretic criterion that selects the triplet whose answer leads to the highest expected gain in information about the classes of a set of examples. Directly applying the proposed criterion requires examining @math triplets with @math instances, which is prohibitive even for datasets of moderate size. We show that a randomized selection strategy can be used to reduce the selection pool from @math to @math , allowing us to scale up to larger-size problems. Experiments show that the proposed method consistently outperforms two baseline policies.
Distance metric learning with relative comparisons has also been studied in different contexts @cite_5 @cite_7 . formulated a constrained optimization problem where the constraints are defined by relative comparisons and the objective is to learn a distance metric that remains as close to an un-weighted Euclidean metric as possible @cite_7 . @cite_5 proposed to learn a projection matrix from relative comparisons. This approach also employed relative comparisons to create constraints on the solution space, but optimized a different objective to encourage sparsity of the learned projection matrix. Both studies assumed that the relative comparisons are given and the constraints are a set of random or otherwise non-optimized set of pre-selected triplets. That is, the algorithm is not allowed to request comparisons outside of the given set.
@cite_5 @cite_7
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We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. 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. Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matrices is not appropriate, because the difference of SPD matrices can be a non-SPD matrix and thus the obtained solution can be uninterpretable. To cope with this problem, we propose to use a properly parameterized LogEuclidean distance and optimize the metric with respect to kernel-target alignment, which is a supervised criterion for kernel learning. Then the resulting non-trivial optimization problem is solved by utilizing the Riemannian geometry. Finally, we experimentally demonstrate the usefulness of our LogEuclidean metric learning algorithm on real-world classification tasks for EEG signals and texture patches. 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.