The past decade has witnessed the rapid development of feature representation learning and distance metric learning, whereas the two steps are often discussed separately. To explore their interaction, this work proposes an end-to-end learning framework called DARI, i.e. Distance metric And Representation Integration, and validates the effectiveness of DARI in the challenging task of person verification. Given the training images annotated with the labels, we first produce a large number of triplet units, and each one contains three images, i.e. one person and the matched mismatch references. For each triplet unit, the distance disparity between the matched pair and the mismatched pair tends to be maximized. We solve this objective by building a deep architecture of convolutional neural networks. In particular, the Mahalanobis distance matrix is naturally factorized as one top fully-connected layer that is seamlessly integrated with other bottom layers representing the image feature. The image feature and the distance metric can be thus simultaneously optimized via the one-shot backward propagation. On several public datasets, DARI shows very promising performance on re-identifying individuals cross cameras against various challenges, and outperforms other state-of-the-art approaches.
A number of approaches, e.g., local metric learning and kernelized metric learning, have been suggested to learn multiple or nonlinear metrics from training data with complicated nonlinear manifold structure. In local metric learning, local metrics can be learned independently for each region or by considering the data manifold structure @cite_34 @cite_28 @cite_29 . In kernelized metric learning, a kernel function is exploited to implicitly embed instances into the reproducing kernel Hilbert space (RKHS), and a Mahalanobis distance metric is then learned in the RKHS space @cite_3 . Actually, kernelized method with Gaussian RBF kernel can also be treated as local learning approach. As pointed out in @cite_4 , local learning are also shallow models, and generally are insufficient in coping with highly varying appearance and deformations of images. Another efficient local distance metric learning @cite_6 was also proposed for classification and retrieval. To handle heterogeneous data, @cite_16 propose a method using a random forest-based classifier to strengthen the distance function with implicit pairwise position dependence.
@cite_4 @cite_28 @cite_29 @cite_3 @cite_6 @cite_16 @cite_34
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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 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). Metric learning has become a very active research field. The most popular representative–Mahalanobis metric learning–can be seen as learning a linear transformation and then computing the Euclidean metric in the transformed space. Since a linear transformation might not always be appropriate for a given learning problem, kernelized versions of various metric learning algorithms exist. However, the problem then becomes finding the appropriate kernel function. Multiple kernel learning addresses this limitation by learning a linear combination of a number of predefined kernels; this approach can be also readily used in the context of multiple-source learning to fuse different data sources. Surprisingly, and despite the extensive work on multiple kernel learning for SVMs, there has been no work in the area of metric learning with multiple kernel learning. In this paper we fill this gap and present a general approach for metric learning with multiple kernel learning. Our approach can be instantiated with different metric learning algorithms provided that they satisfy some constraints. Experimental evidence suggests that our approach outperforms metric learning with an unweighted kernel combination and metric learning with cross-validation based kernel selection. We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several large-scale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner.