Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.
The large margin nearest neighbours (LMNN) @cite_14 algorithm employs semidefinite programming to optimise a loss function composed of two terms. Specifically, there are two evaluations of Equation . One term draws very similar instances together, and the other encourages a margin to be formed between dissimilar instances. As the name suggests, the motivation for the development of this algorithm was to improve the accuracy of @math -Nearest Neighbours ( @math -NN) classifiers.
@cite_14
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Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a much stronger relation than what is commonly thought. We analyze SVMs from a metric learning perspective and cast them as a metric learning problem, a view which helps us uncover the relations of the two algorithms. We show that LMNN can be seen as learning a set of local SVM-like models in a quadratic space. Along the way and inspired by the metric-based interpretation of SVM s we derive a novel variant of SVMs, epsilon-SVM, to which LMNN is even more similar. We give a unified view of LMNN and the different SVM variants. Finally we provide some preliminary experiments on a number of benchmark datasets in which show that epsilon-SVM compares favorably both with respect to LMNN and SVM. This paper presents a new method for viewpoint invariant pedestrian recognition problem. We use a metric learning framework to obtain a robust metric for large margin nearest neighbor classification with rejection (i.e., classifier will return no matches if all neighbors are beyond a certain distance). The rejection condition necessitates the use of a uniform threshold for a maximum allowed distance for deeming a pair of images a match. In order to handle the rejection case, we propose a novel cost similar to the Large Margin Nearest Neighbor (LMNN) method and call our approach Large Margin Nearest Neighbor with Rejection (LMNN-R). Our method is able to achieve significant improvement over previously reported results on the standard Viewpoint Invariant Pedestrian Recognition (VIPeR [1]) dataset. This paper presents a relational framework for studying properties of labeled data points related to proximity and labeling information in order to improve the performance of the 1NN rule. Specifically, the class conditional nearest neighbor (ccnn) relation over pairs of points in a labeled training set is introduced. For a given class label c, this relation associates to each point a its nearest neighbor computed among only those points with class label c (excluded a). A characterization of ccnn in terms of two graphs is given. These graphs are used for defining a novel scoring function over instances by means of an information-theoretic divergence measure applied to the degree distributions of these graphs. The scoring function is employed to develop an effective large margin instance selection method, which is empirically demonstrated to improve storage and accuracy performance of the 1NN rule on artificial and real-life data sets. We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm).