A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a number of methods have been proposed to efficiently learn it. However, the nature of the problem makes it quite difficult for large scale data, as well as data for which classes overlap. This paper presents a simple way of improving accuracy and scalability of any iterative metric learning algorithm, where constraints are obtained prior to the algorithm. The proposed approach relies on a loss-dependent weighted selection of constraints that are used for learning the metric. Using the corresponding dedicated loss function, the method clearly allows to obtain better results than state-of-the-art methods, both in terms of accuracy and time complexity. Some experimental results on real world, and potentially large, datasets are demonstrating the effectiveness of our proposition.
Finally, note that we restrict here to the description of global metric learning algorithms: a unique metric matrix @math is learned for the entire data set. Some other approaches propose to learn a matrix by class @cite_30 , or multi-task metrics @cite_17 . Naturally, the proposition could also be used with non linear (i.e. kernelized or local metric learning, see e.g. @cite_14 , @cite_23 ) methods.
@cite_30 @cite_14 @cite_23 @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. 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. 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). Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data. We consider the problem of learning a local metric in order to enhance the performance of nearest neighbor classification. Conventional metric learning methods attempt to separate data distributions in a purely discriminative manner; here we show how to take advantage of information from parametric generative models. We focus on the bias in the information-theoretic error arising from finite sampling effects, and find an appropriate local metric that maximally reduces the bias based upon knowledge from generative models. As a byproduct, the asymptotic theoretical analysis in this work relates metric learning to dimensionality reduction from a novel perspective, which was not understood from previous discriminative approaches. Empirical experiments show that this learned local metric enhances the discriminative nearest neighbor performance on various datasets using simple class conditional generative models such as a Gaussian. 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. 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. As we enter into the big data age and an avalanche of images have become readily available, recognition systems face the need to move from close, lab settings where the number of classes and training data are fixed, to dynamic scenarios where the number of categories to be recognized grows continuously over time, as well as new data providing useful information to update the system. Recent attempts, like the open world recognition framework, tried to inject dynamics into the system by detecting new unknown classes and adding them incrementally, while at the same time continuously updating the models for the known classes. incrementally adding new classes and detecting instances from unknown classes, while at the same time continuously updating the models for the known classes. In this paper we argue that to properly capture the intrinsic dynamic of open world recognition, it is necessary to add to these aspects (a) the incremental learning of the underlying metric, (b) the incremental estimate of confidence thresholds for the unknown classes, and (c) the use of local learning to precisely describe the space of classes. We extend three existing metric learning algorithms towards these goals by using online metric learning. Experimentally we validate our approach on two large-scale datasets in different learning scenarios. For all these scenarios our proposed methods outperform their non-online counterparts. We conclude that local and online learning is important to capture the full dynamics of open world recognition. Linear metric learning is a widely used methodology to learn a dissimilarity function from a set of similar dissimilar example pairs. Using a single metric may be a too restrictive assumption when handling heterogeneous datasets. Recently, local metric learning methods have been introduced to overcome this limitation. However, they are subjects to constraints preventing their usage in many applications. For example, they require knowledge of the class label of the training points. In this paper, we present a novel local metric learning method, which overcomes some limitations of previous approaches. The method first computes a Gaussian Mixture Model from a low dimensional embedding of training data. Then it estimates a set of local metrics by solving a convex optimization problem; finally, a dissimilarity function is obtained by aggregating the local metrics. Our experiments show that the proposed method achieves state-of-the-art results on four datasets. Metric and kernel learning arise in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points. In this paper, we study the connections between metric learning and kernel learning that arise when studying metric learning as a linear transformation learning problem. In particular, we propose a general optimization framework for learning metrics via linear transformations, and analyze in detail a special case of our framework-that of minimizing the LogDet divergence subject to linear constraints. We then propose a general regularized framework for learning a kernel matrix, and show it to be equivalent to our metric learning framework. Our theoretical connections between metric and kernel learning have two main consequences: 1) the learned kernel matrix parameterizes a linear transformation kernel function and can be applied inductively to new data points, 2) our result yields a constructive method for kernelizing most existing Mahalanobis metric learning formulations. We demonstrate our learning approach by applying it to large-scale real world problems in computer vision, text mining and semi-supervised kernel dimensionality reduction. In this paper, we introduce two novel metric learning algorithms, Χ2-LMNN and GB-LMNN, which are explicitly designed to be non-linear and easy-to-use. The two approaches achieve this goal in fundamentally different ways: Χ2-LMNN inherits the computational benefits of a linear mapping from linear metric learning, but uses a non-linear Χ2-distance to explicitly capture similarities within histogram data sets; GB-LMNN applies gradient-boosting to learn non-linear mappings directly in function space and takes advantage of this approach's robustness, speed, parallelizability and insensitivity towards the single additional hyper-parameter. On various benchmark data sets, we demonstrate these methods not only match the current state-of-the-art in terms of kNN classification error, but in the case of Χ2-LMNN, obtain best results in 19 out of 20 learning settings. The objective of sparse metric learning is to learn a distance measure from a set of data in addition to finding a low-dimensional representation. Despite demonstrated success, the performance of existing sparse metric learning approaches is usually limited because the methods assumes certain problem relaxations or they target the SML objective indirectly. In this paper, we propose a Generalized Sparse Metric Learning method. This novel framework offers a unified view for understanding many existing sparse metric learning algorithms including the Sparse Metric Learning framework proposed in (Rosales and Fung ACM International conference on knowledge discovery and data mining (KDD), pp 367–373, 2006), the Large Margin Nearest Neighbor ( in Advances in neural information processing systems (NIPS), 2006; Weinberger and Saul in Proceedings of the twenty-fifth international conference on machine learning (ICML-2008), 2008), and the D-ranking Vector Machine (D-ranking VM) (Ouyang and Gray in Proceedings of the twenty-fifth international conference on machine learning (ICML-2008), 2008). Moreover, GSML also establishes a close relationship with the Pairwise Support Vector Machine ( in BMC Bioinform, 8, 2007). Furthermore, the proposed framework is capable of extending many current non-sparse metric learning models to their sparse versions including Relevant Component Analysis (Bar- in J Mach Learn Res, 6:937–965, 2005) and a state-of-the-art method proposed in ( Advances in neural information processing systems (NIPS), 2002). We present the detailed framework, provide theoretical justifications, build various connections with other models, and propose an iterative optimization method, making the framework both theoretically important and practically scalable for medium or large datasets. Experimental results show that this generalized framework outperforms six state-of-the-art methods with higher accuracy and significantly smaller dimensionality for seven publicly available datasets. The metric learning problem is concerned with learning a distance function tuned to a particular task, and has been shown to be useful when used in conjunction with nearest-neighbor methods and other techniques that rely on distances or similarities. This survey presents an overview of existing research in metric learning, including recent progress on scaling to high-dimensional feature spaces and to data sets with an extremely large number of data points. A goal of the survey is to present as unified as possible a framework under which existing research on metric learning can be cast. The first part of the survey focuses on linear metric learning approaches, mainly concentrating on the class of Mahalanobis distance learning methods. We then discuss nonlinear metric learning approaches, focusing on the connections between the nonlinear and linear approaches. Finally, we discuss extensions of metric learning, as well as applications to a variety of problems in computer vision, text analysis, program analysis, and multimedia. Full text available at: http: dx.doi.org 10.1561 2200000019 Metric learning is a fundamental problem in computer vision. Different features and algorithms may tackle a problem from different angles, and thus often provide complementary information. In this paper, we propose a fusion algorithm which outputs enhanced metrics by combining multiple given metrics (similarity measures). Unlike traditional co-training style algorithms where multi-view features or multiple data subsets are used for classification or regression, we focus on fusing multiple given metrics through diffusion process in an unsupervised way. Our algorithm has its particular advantage when the input similarity matrices are the outputs from diverse algorithms. We provide both theoretical and empirical explanations to our method. Significant improvements over the state-of-the-art results have been observed on various benchmark datasets. For example, we have achieved 100 accuracy (no longer the bull's eye measure) on the MPEG-7 shape dataset. Our method has a wide range of applications in machine learning and computer vision. We study metric learning as a problem of information retrieval. We present a general metric learning algorithm, based on the structural SVM framework, to learn a metric such that rankings of data induced by distance from a query can be optimized against various ranking measures, such as AUC, Precision-at-k, MRR, MAP or NDCG. We demonstrate experimental results on standard classification data sets, and a large-scale online dating recommendation problem. The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (, 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW). Metric learning methods, for person re-identification, estimate a scaling for distances in a vector space that is optimized for picking out observations of the same individual. This paper presents a novel approach to the pedestrian re-identification problem that uses metric learning to improve the state-of-the-art performance on standard public datasets. Very high dimensional features are extracted from the source color image. A first processing stage performs unsupervised PCA dimensionality reduction, constrained to maintain the redundancy in color-space representation. A second stage further reduces the dimensionality, using a Local Fisher Discriminant Analysis defined by a training set. A regularization step is introduced to avoid singular matrices during this stage. The experiments conducted on three publicly available datasets confirm that the proposed method outperforms the state-of-the-art performance, including all other known metric learning methods. Further-more, the method is an effective way to process observations comprising multiple shots, and is non-iterative: the computation times are relatively modest. Finally, a novel statistic is derived to characterize the Match Characteristic: the normalized entropy reduction can be used to define the 'Proportion of Uncertainty Removed' (PUR). This measure is invariant to test set size and provides an intuitive indication of performance. A new deep multitask learning based metric learning method is proposed.An appropriate architecture is proposed for offline signature verification.The knowledge of other signers' samples is transfered for better accuracy.The proposed method outperforms SVM and Discriminative Deep Metric Learning.It outperforms the accuracy of other published reports. Display Omitted This paper presents a novel classification method, Deep Multitask Metric Learning (DMML), for offline signature verification. Unlike existing methods that to verify questioned signatures of an individual merely consider the training samples of that class, DMML uses the knowledge from the similarities and dissimilarities between the genuine and forged samples of other classes too. To this end, using the idea of multitask and transfer learning, DMML train a distance metric for each class together with other classes simultaneously. DMML has a structure with a shared layer acting as a writer-independent approach, that is followed by separated layers which learn writer-dependent factors. We compare the proposed method against SVM, writer-dependent and writer-independent Discriminative Deep Metric Learning method on four offline signature datasets (UTSig, MCYT-75, GPDSsynthetic, and GPDS960GraySignatures) using Histogram of Oriented Gradients (HOG) and Discrete Radon Transform (DRT) features. Results of our experiments show that DMML achieves better performance compared to other methods in verifying genuine signatures, skilled and random forgeries. 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.