We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on similar and dissimilar pairs while training. The proposed method is derived by an approximate kernelization of a linear Mahalanobis-like distance metric learning algorithm and can also be seen as a kernel neural network. The number of model parameters and test time evaluation complexity of the proposed method are O(dD) where D is the dimensionality of the input features and d is the dimension of the projection space - this is in contrast to the usual kernelization methods as, unlike them, the complexity does not scale linearly with the number of training examples. We propose a stochastic gradient based learning algorithm which makes the method scalable (w.r.t. the number of training examples), while being nonlinear. We train the method with up to half a million training pairs of 4096 dimensional CNN features. We give empirical comparisons with relevant baselines on seven challenging datasets for the task of low dimensional semantic category based image retrieval.
Most of the initial metric learning methods were linear, the semidefinite programming formulation by Xing al @cite_61 , large margin formulation for @math -NN classification by Weinberger al @cite_2 , collapsing classes' formulation (make the distance between vectors of same class zero and between those of different classes large) of Globerson and Roweis @cite_13 and neighbourhood component analysis of Goldberger al @cite_22 .
@cite_61 @cite_13 @cite_22 @cite_2
2808979505 2104752854 1674203940 2949579938
Abstract Distance metric learning has been a hot research spot recently due to its high effectiveness and efficiency in improving the performance of distance related methods, such as k nearest neighbors ( k NN). Metric learning aims to learn a data-dependent metric to make intra-class distance smaller and inter-class larger. A large number of methods have been proposed for various applications and a survey to evaluate and compare these methods is imperative. The existing surveys just analyze the algorithms theoretically or compare them experimentally with a narrow time scope. Therefore, the paper reviews classical and influential methods that were proposed between 2003 and 2017 and presents a taxonomy based on the most distinct character of each method. All the methods are categorized into five classes, including pairwise cost, probabilistic framework, boost-like approaches, advantageous variants and specific applications. A comprehensive experimental study is made to compare all the selected methods, exploring the ability in improving accuracy, the relation between distance change and accuracy, the relation between accuracy and k NN neighbor size. We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by trying to collapse all examples in the same class to a single point and push examples in other classes infinitely far away. We show that when the metric we learn is used in simple classifiers, it yields substantial improvements over standard alternatives on a variety of problems. We also discuss how the learned metric may be used to obtain a compact low dimensional feature representation of the original input space, allowing more efficient classification with very little reduction in performance. 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. 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.