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, the authors, in @cite_6 , propose a boosting-like algorithm for metric learning. While the idea of using the principle of boosting is similar to our proposition, they are using it to decompose the learning process to a linear positive combination of rank-one matrices, instead of setting local weights to individuals as in our approach. Consequently, the two methods do not focus on the same points, and may even be used together to produce an even more fast metric learning algorithm.
@cite_6
1544007523 2130318956 2949579938 2112076978 2142863987 2103504567 2024046085 2950690897 1674203940 2115669554 2153656574 2800513603 2586258914 2121805075 2009228073 2140376886 2903034054 2605102252 2010990026 2005118650
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. 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. 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. In an earlier paper, we introduced a new "boosting" algorithm called AdaBoost which, theoretically, can be used to significantly reduce the error of any learning algorithm that con- sistently generates classifiers whose performance is a little better than random guessing. We also introduced the related notion of a "pseudo-loss" which is a method for forcing a learning algorithm of multi-label concepts to concentrate on the labels that are hardest to discriminate. In this paper, we describe experiments we carried out to assess how well AdaBoost with and without pseudo-loss, performs on real learning problems. We performed two sets of experiments. The first set compared boosting to Breiman's "bagging" method when used to aggregate various classifiers (including decision trees and single attribute- value tests). We compared the performance of the two methods on a collection of machine-learning benchmarks. In the second set of experiments, we studied in more detail the performance of boosting using a nearest-neighbor classifier on an OCR problem. 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. Boosting algorithms and successful applications thereof abound for classification and regression learning problems, but not for unsupervised learning. We propose a sequential approach to adding features to a random field model by training them to improve classification performance between the data and an equal-sized sample of "negative examples" generated from the model's current estimate of the data density. Training in each boosting round proceeds in three stages: first we sample negative examples from the model's current Boltzmann distribution. Next, a feature is trained to improve classification performance between data and negative examples. Finally, a coefficient is learned which determines the importance of this feature relative to ones already in the pool. Negative examples only need to be generated once to learn each new feature. The validity of the approach is demonstrated on binary digits and continuous synthetic data. Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of well-known statistical principles, namely additive modeling and maximum likelihood. For the two-class problem, boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum Bernoulli likelihood as a criterion. We develop more direct approximations and show that they exhibit nearly identical results to boosting. Direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations, and far superior in some. We suggest a minor modification to boosting that can reduce computation, often by factors of 10 to 50. Finally, we apply these insights to produce an alternative formulation of boosting decision trees. This approach, based on best-first truncated tree induction, often leads to better performance, and can provide interpretable descriptions of the aggregate decision rule. It is also much faster computationally, making it more suitable to large-scale data mining applications. 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 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. We consider the problem of learning an unknown large-margin halfspace in the context of parallel computation, giving both positive and negative results. As our main positive result, we give a parallel algorithm for learning a large-margin half-space, based on an algorithm of Nesterov's that performs gradient descent with a momentum term. We show that this algorithm can learn an unknown γ-margin halfspace over n dimensions using n ċ poly(1 γ) processors and running in time O(1 γ)+O(log n). In contrast, naive parallel algorithms that learn a γ-margin halfspace in time that depends polylogarithmically on n have an inverse quadratic running time dependence on the margin parameter γ. Our negative result deals with boosting, which is a standard approach to learning large-margin halfspaces. We prove that in the original PAC framework, in which a weak learning algorithm is provided as an oracle that is called by the booster, boosting cannot be parallelized. More precisely, we show that, if the algorithm is allowed to call the weak learner multiple times in parallel within a single boosting stage, this ability does not reduce the overall number of successive stages of boosting needed for learning by even a single stage. Our proof is information-theoretic and does not rely on unproven assumptions. Metric learning aims to construct an embedding where two extracted features corresponding to the same identity are likely to be closer than features from different identities. This paper presents a method for learning such a feature space where the cosine similarity is effectively optimized through a simple re-parametrization of the conventional softmax classification regime. At test time, the final classification layer can be stripped from the network to facilitate nearest neighbor queries on unseen individuals using the cosine similarity metric. This approach presents a simple alternative to direct metric learning objectives such as siamese networks that have required sophisticated pair or triplet sampling strategies in the past. The method is evaluated on two large-scale pedestrian re-identification datasets where competitive results are achieved overall. In particular, we achieve better generalization on the test set compared to a network trained with triplet loss. 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. Several authors have suggested viewing boosting as a gradient descent search for a good fit in function space. We apply gradient-based boosting methodology to the unsupervised learning problem of density estimation. We show convergence properties of the algorithm and prove that a strength of weak learnability property applies to this problem as well. We illustrate the potential of this approach through experiments with boosting Bayesian networks to learn density models. 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. 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. Deep metric learning aims to learn a function mapping image pixels to embedding feature vectors that model the similarity between images. The majority of current approaches are non-parametric, learning the metric space directly through the supervision of similar (pairs) or relatively similar (triplets) sets of images. A difficult challenge for training these approaches is mining informative samples of images as the metric space is learned with only the local context present within a single mini-batch. Alternative approaches use parametric metric learning to eliminate the need for sampling through supervision of images to proxies. Although this simplifies optimization, such proxy-based approaches have lagged behind in performance. In this work, we demonstrate that a standard classification network can be transformed into a variant of proxy-based metric learning that is competitive against non-parametric approaches across a wide variety of image retrieval tasks. We address key challenges in proxy-based metric learning such as performance under extreme classification and describe techniques to stabilize and learn higher dimensional embeddings. We evaluate our approach on the CAR-196, CUB-200-2011, Stanford Online Product, and In-Shop datasets for image retrieval and clustering. Finally, we show that our softmax classification approach can learn high-dimensional binary embeddings that achieve new state-of-the-art performance on all datasets evaluated with a memory footprint that is the same or smaller than competing approaches. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. 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. 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).