For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance.
Metric learning is an active research field with many algorithms, generally divided into linear @cite_20 which learn a Mahalanobis distance, non-linear @cite_12 that learn a nonlinear transformation and use @math distance on the transformed space, and local which learn a metric per datum. The LMNN and MLMM @cite_20 algorithm are considered the leading metric learning method. For a recent comprehensive survey that covers linear, non-linear and local methods see @cite_19 .
@cite_19 @cite_12 @cite_20
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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 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 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. The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner. The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come. This paper introduces a novel classification approach which improves the performance of support vector machines (SVMs) by learning a distance metric. The metric learned is a Mahalanobis metric previously trained so that examples from different classes are separated with a large margin. The learned metric is used to define a kernel function for SVM classification. In this context, the metric can be seen as a linear transformation of the original inputs before applying an SVM classifier that uses Euclidean distances. This transformation increases the separability of classes in the transformed space where the classification is applied. Experiments demonstrate significant improvements in classification tasks on various data sets. Face verification is the task of determining by analyzing face images, whether a person is who he she claims to be. It is a very challenge problem, due to large variations in lighting, background, expression, hairstyle and occlusion. The crucial problem is to compute the similarity of two face vectors. Metric learning has provides a viable solution to this problem. Until now, many metric learning algorithms have been proposed, but they are usually limited to learning a linear transformation (i.e. finding a global Mahalanobis metric). In this brief, we propose a nonlinear metric learning method, which learns an explicit mapping from the original space to an optimal subspace, using deep Independent Subspace Analysis network. Compared to kernel methods, which can also learn nonlinear transformations, our method is a deep and local learning architecture, and therefore exhibits more powerful ability to learn the nature of highly variable dataset. We evaluate our method on the LFW benchmark, and results show very comparable performance to the state-of-art methods (achieving 92.28 accuracy), while maintaining simplicity and good generalization ability. 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. We introduce a method that enables scalable image search for learned metrics. Given pairwise similarity and dissimilarity constraints between some images, we learn a Mahalanobis distance function that captures the imagespsila underlying relationships well. To allow sub-linear time similarity search under the learned metric, we show how to encode the learned metric parameterization into randomized locality-sensitive hash functions. We further formulate an indirect solution that enables metric learning and hashing for vector spaces whose high dimensionality make it infeasible to learn an explicit weighting over the feature dimensions. We demonstrate the approach applied to a variety of image datasets. Our learned metrics improve accuracy relative to commonly-used metric baselines, while our hashing construction enables efficient indexing with learned distances and very large databases. In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction. We address the problem of learning distance metrics using side-information in the form of groups of "similar" points. We propose to use the RCA algorithm, which is a simple and efficient algorithm for learning a full ranked Mahalanobis metric (, 2002). We first show that RCA obtains the solution to an interesting optimization problem, founded on an information theoretic basis. If the Mahalanobis matrix is allowed to be singular, we show that Fisher's linear discriminant followed by RCA is the optimal dimensionality reduction algorithm under the same criterion. We then show how this optimization problem is related to the criterion optimized by another recent algorithm for metric learning (, 2002), which uses the same kind of side information. We empirically demonstrate that learning a distance metric using the RCA algorithm significantly improves clustering performance, similarly to the alternative algorithm. Since the RCA algorithm is much more efficient and cost effective than the alternative, as it only uses closed form expressions of the data, it seems like a preferable choice for the learning of full rank Mahalanobis distances. We introduce a method that enables scalable similarity search for learned metrics. Given pairwise similarity and dissimilarity constraints between some examples, we learn a Mahalanobis distance function that captures the examples' underlying relationships well. To allow sublinear time similarity search under the learned metric, we show how to encode the learned metric parameterization into randomized locality-sensitive hash functions. We further formulate an indirect solution that enables metric learning and hashing for vector spaces whose high dimensionality makes it infeasible to learn an explicit transformation over the feature dimensions. We demonstrate the approach applied to a variety of image data sets, as well as a systems data set. The learned metrics improve accuracy relative to commonly used metric baselines, while our hashing construction enables efficient indexing with learned distances and very large databases. During last decade, tremendous efforts have been devoted to the research of time series classification. Indeed, many previous works suggested that the simple nearest-neighbor classification is effective and difficult to beat. However, we usually need to determine the distance metric (e.g., Euclidean distance and Dynamic Time Warping) for different domains, and current evidence shows that there is no distance metric that is best for all time series data. Thus, the choice of distance metric has to be done empirically, which is time expensive and not always effective. To automatically determine the distance metric, in this paper, we investigate the distance metric learning and propose a novel Convolutional Nonlinear Neighbourhood Components Analysis model for time series classification. Specifically, our model performs supervised learning to project original time series into a transformed space. When classifying, nearest neighbor classifier is then performed in this transformed space. Finally, comprehensive experimental results demonstrate that our model can improve the classification accuracy to some extent, which indicates that it can learn a good distance metric. The dynamic feasibility of solutions to motion planning problems using Rapidly Exploring Random Trees depends strongly on the choice of the distance metric used while planning. The ideal distance metric is the optimal cost of traversal between two states in the state space. However, it is computationally intensive to find the optimal cost while planning. We propose a novel approach to overcome this barrier by using a supervised learning algorithm that learns a nonlinear function which is an estimate of the optimal cost, via offline training. We use the Iterative Linear Quadratic Regulator approach for estimating an approximation to the optimal cost and learn this cost using Locally Weighted Projection Regression. We show that the learnt function approximates the original cost with a reasonable tolerance and more importantly, gives a tremendous speed up of a factor of 1000 over the actual computation time. We also use the learnt metric for solving the pendulum swing up planning problem and show that our metric performs better than the popularly used Linear Quadratic Regulator based metric. Recent years have witnessed extensive studies on distance metric learning (DML) for improving similarity search in multimedia information retrieval tasks. Despite their successes, most existing DML methods suffer from two critical limitations: (i) they typically attempt to learn a linear distance function on the input feature space, in which the assumption of linearity limits their capacity of measuring the similarity on complex patterns in real-world applications; (ii) they are often designed for learning distance metrics on uni-modal data, which may not effectively handle the similarity measures for multimedia objects with multimodal representations. To address these limitations, in this paper, we propose a novel framework of online multimodal deep similarity learning (OMDSL), which aims to optimally integrate multiple deep neural networks pretrained with stacked denoising autoencoder. In particular, the proposed framework explores a unified two-stage online learning scheme that consists of (i) learning a flexible nonlinear transformation function for each individual modality, and (ii) learning to find the optimal combination of multiple diverse modalities simultaneously in a coherent process. We conduct an extensive set of experiments to evaluate the performance of the proposed algorithms for multimodal image retrieval tasks, in which the encouraging results validate the effectiveness of the proposed technique. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BOOSTMETRIC, for learning a quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive semidefinite. Semidefinite programming is often used to enforce this constraint, but does not scale well and is not easy to implement. BOOSTMETRIC is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace-one rank-one matrices. BOOSTMETRIC thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting methods are easy to implement, efficient, and can accommodate various types of constraints. We extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor. Experiments on various data sets demonstrate that the proposed algorithms compare favorably to those state-of-the-art methods in terms of classification accuracy and running time. The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed BOOSTMETRIC, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. BOOSTMETRIC is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. BOOSTMETRIC thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time. This paper presents a new discriminative deep metric learning (DDML) method for face verification in the wild. Different from existing metric learning-based face verification methods which aim to learn a Mahalanobis distance metric to maximize the inter-class variations and minimize the intra-class variations, simultaneously, the proposed DDML trains a deep neural network which learns a set of hierarchical nonlinear transformations to project face pairs into the same feature subspace, under which the distance of each positive face pair is less than a smaller threshold and that of each negative pair is higher than a larger threshold, respectively, so that discriminative information can be exploited in the deep network. Our method achieves very competitive face verification performance on the widely used LFW and YouTube Faces (YTF) datasets. Metric learning algorithms can provide useful distance functions for a variety of domains, and recent work has shown good accuracy for problems where the learner can access all distance constraints at once. However, in many real applications, constraints are only available incrementally, thus necessitating methods that can perform online updates to the learned metric. Existing online algorithms offer bounds on worst-case performance, but typically do not perform well in practice as compared to their offline counterparts. We present a new online metric learning algorithm that updates a learned Mahalanobis metric based on LogDet regularization and gradient descent. We prove theoretical worst-case performance bounds, and empirically compare the proposed method against existing online metric learning algorithms. To further boost the practicality of our approach, we develop an online locality-sensitive hashing scheme which leads to efficient updates to data structures used for fast approximate similarity search. We demonstrate our algorithm on multiple datasets and show that it outperforms relevant baselines.