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.
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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. Achieving high match accuracy for a large variety of ontologies, considering a single matcher is often not sufficient for high match quality. Therefore, combining the corresponding weights for different semantic aspects, reflecting their different importance or contributions becomes unavoidable for ontology matching. Combining multiple measures into a single similarity metric has been traditionally solved using weights determined manually by an expert, or calculated through general methods e.g. average or sigmoid function, however this does not provide a flexible and self-configuring matching tool. In this paper, an intelligent combination using Artificial Neural Network ANN as a machine learning-based method to ascertain how to combine multiple similarity measures into a single aggregated metric with the final aim of improving the ontology alignment quality is proposed. XMap++ is applied to benchmark and anatomy tests at OAEI campaign 2012. Results show that neural network boosts the performance in most cases, and that the proposed novel approach is competitive with top-ranked system. Boosted decision trees are among the most popular learning techniques in use today. While exhibiting fast speeds at test time, relatively slow training renders them impractical for applications with real-time learning requirements. We propose a principled approach to overcome this drawback. We prove a bound on the error of a decision stump given its preliminary error on a subset of the training data; the bound may be used to prune unpromising features early in the training process. We propose a fast training algorithm that exploits this bound, yielding speedups of an order of magnitude at no cost in the final performance of the classifier. Our method is not a new variant of Boosting; rather, it is used in conjunction with existing Boosting algorithms and other sampling methods to achieve even greater speedups. Which seems more suspicious: 5,000 tweets from 200 users on 5 IP addresses, or 10,000 tweets from 500 users on 500 IP addresses but all with the same trending topic and all in 10 minutes? The literature has many methods that try to find dense blocks in matrices, and, recently, tensors, but no method gives a principled way to score the suspiciouness of dense blocks with different numbers of modes and rank them to draw human attention accordingly. Dense blocks are worth inspecting, typically indicating fraud, emerging trends, or some other noteworthy deviation from the usual. Our main contribution is that we show how to unify these methods and how to give a principled answer to questions like the above. Specifically, (a) we give a list of axioms that any metric of suspicousness should satisfy, (b) we propose an intuitive, principled metric that satisfies the axioms, and is fast to compute, (c) we propose CROSSSPOT, an algorithm to spot dense regions, and sort them in importance ("suspiciousness") order. Finally, we apply CROSSSPOT to real data, where it improves the F1 score over previous techniques by 68 and finds retweet-boosting in a real social dataset spanning 0.3 billion posts. 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 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. This paper describes a new technique for solv- ing multiclass learning problems by combining Freund and Schapire's boosting algorithm with the main ideas of Diet- terich and Bakiri's method of error-correcting output codes (ECOC). Boosting is a general method of improving the ac- curacy of a given base or "weak" learning algorithm. ECOC is a robust method of solving multiclass learning problems by reducing to a sequence of two-class problems. We show that our new hybrid method has advantages of both: Like ECOC, our method only requires that the base learning al- gorithm work on binary-labeled data. Like boosting, we prove that the method comes with strong theoretical guar- antees on the training and generalization error of the final combined hypothesis assuming only that the base learning algorithm perform slightly better than random guessing. Although previous methods were known for boosting multi- class problems, the new method may be significantly faster and require less programming effort in creating the base learning algorithm. We also compare the new algorithm experimentally to other voting methods. Defining a suitable metric is one of the biggest challenges in deformable image fusion from different modalities. In this paper, we propose a novel approach for multi-modal metric learning in the deformable registration framework that consists of embedding data from both modalities into a common metric space whose metric is used to parametrize the similarity. Specifically, we use image representation in the Fourier Gabor space which introduces invariance to the local pose parameters, and the Hamming metric as the target embedding space, which allows constructing the embedding using boosted learning algorithms. The resulting metric is incorporated into a discrete optimization framework. Very promising results demonstrate the potential of the proposed method. Image auto-annotation is an important open problem in computer vision. For this task we propose TagProp, a discriminatively trained nearest neighbor model. Tags of test images are predicted using a weighted nearest-neighbor model to exploit labeled training images. Neighbor weights are based on neighbor rank or distance. TagProp allows the integration of metric learning by directly maximizing the log-likelihood of the tag predictions in the training set. In this manner, we can optimally combine a collection of image similarity metrics that cover different aspects of image content, such as local shape descriptors, or global color histograms. We also introduce a word specific sigmoidal modulation of the weighted neighbor tag predictions to boost the recall of rare words. We investigate the performance of different variants of our model and compare to existing work. We present experimental results for three challenging data sets. On all three, TagProp makes a marked improvement as compared to the current state-of-the-art. Many real-world objects described by multiple attributes or features can be decomposed as multiple "views" (e.g., an image can be described by a color view or a shape view), which often provides complementary information to each other. Learning a metric (similarity measures) for multi-view data is primary due to its wide applications in practices. However, leveraging multi-view information to produce a good metric is a great challenge and existing techniques are concerned with pairwise similarities, leading to undesirable fusion metric and high computational complexity. In this paper, we propose a novel Metric Fusion technique via cross-view graph Random Walk, named MFRW, regarding a multi-view based similarity graphs (with each similarity graph constructed under each view). Instead of using pairwise similarities, we seek a high-order metric yielded by graph random walks over constructed similarity graphs. Observing that outlier views" may exist in the fusion process, we incorporate the coefficient matrices representing the correlation strength between any two views into MFRW, named WMFRW. The principle of WMFRW is implemented by exploring the common latent structure" between views. The empirical studies conducted on real-world databases demonstrate that our approach outperforms the state-of-the-art competitors in terms of effectiveness and efficiency. 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. The modern image search system requires semantic understanding of image, and a key yet under-addressed problem is to learn a good metric for measuring the similarity between images. While deep metric learning has yielded impressive performance gains by extracting high level abstractions from image data, a proper objective loss function becomes the central issue to boost the performance. In this paper, we propose a novel angular loss, which takes angle relationship into account, for learning better similarity metric. Whereas previous metric learning methods focus on optimizing the similarity (contrastive loss) or relative similarity (triplet loss) of image pairs, our proposed method aims at constraining the angle at the negative point of triplet triangles. Several favorable properties are observed when compared with conventional methods. First, scale invariance is introduced, improving the robustness of objective against feature variance. Second, a third-order geometric constraint is inherently imposed, capturing additional local structure of triplet triangles than contrastive loss or triplet loss. Third, better convergence has been demonstrated by experiments on three publicly available datasets. Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data are popular to analyze complicated data objects and to cover domain specific data properties. Without an underlying vector space these data are given as pairwise (dis-)similarities only. The few available methods for such data focus widely on similarities and do not scale to large datasets. Kernel methods are very effective for metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nystrom approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs in the number of samples. By the proposed approach effective kernel approaches become accessible. Experiments with several larger (dis-)similarity datasets show that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. The main contribution is an efficient and accurate technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices at linear costs. HighlightsWe propose a linear time and memory efficient approach for converting low rank dissimilarity matrices to similarity matrices and vice versa.Our approach is applicable for proximities obtained from non-metric proximity measures (indefinite kernels, non-standard dissimilarity measures).The presented approach also comprises a generalization of Landmark MDS - the presented approach is in general more accurate and flexible than Landmark MDS.We provide an alternative derivation of the Nystrom approximation together with a convergence proof, also for indefinite kernels not given in the workshop paper as a core element of the approach. Recent studies have shown that boosting provides excellent predictive performance across a wide variety of tasks. In Learning-to-rank, boosted models such as RankBoost and LambdaMART have been shown to be among the best performing learning methods based on evaluations on public data sets. In this paper, we show how the combination of bagging as a variance reduction technique and boosting as a bias reduction technique can result in very high precision and low variance ranking models. We perform thousands of parameter tuning experiments for LambdaMART to achieve a high precision boosting model. Then we show that a bagged ensemble of such LambdaMART boosted models results in higher accuracy ranking models while also reducing variance as much as 50 . We report our results on three public learning-to-rank data sets using four metrics. Bagged LamdbaMART outperforms all previously reported results on ten of the twelve comparisons, and bagged LambdaMART outperforms non-bagged LambdaMART on all twelve comparisons. For example, wrapping bagging around LambdaMART increases NDCG@1 from 0.4137 to 0.4200 on the MQ2007 data set; the best prior results in the literature for this data set is 0.4134 by RankBoost. Learning from imbalanced data sets, where the number of examples of one (majority) class is much higher than the others, presents an important challenge to the machine learning community. Traditional machine learning algorithms may be biased towards the majority class, thus producing poor predictive accuracy over the minority class. In this paper, we describe a new approach that combines boosting, an ensemble-based learning algorithm, with data generation to improve the predictive power of classifiers against imbalanced data sets consisting of two classes. In the DataBoost-IM method, hard examples from both the majority and minority classes are identified during execution of the boosting algorithm. Subsequently, the hard examples are used to separately generate synthetic examples for the majority and minority classes. The synthetic data are then added to the original training set, and the class distribution and the total weights of the different classes in the new training set are rebalanced. The DataBoost-IM method was evaluated, in terms of the F-measures, G-mean and overall accuracy, against seventeen highly and moderately imbalanced data sets using decision trees as base classifiers. Our results are promising and show that the DataBoost-IM method compares well in comparison with a base classifier, a standard benchmarking boosting algorithm and three advanced boosting-based algorithms for imbalanced data set. Results indicate that our approach does not sacrifice one class in favor of the other, but produces high predictions against both minority and majority classes. 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 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. Humans can quickly learn new visual concepts, perhaps because they can easily visualize or imagine what novel objects look like from different views. Incorporating this ability to hallucinate novel instances of new concepts might help machine vision systems perform better low-shot learning, i.e., learning concepts from few examples. We present a novel approach to low-shot learning that uses this idea. Our approach builds on recent progress in meta-learning ("learning to learn") by combining a meta-learner with a "hallucinator" that produces additional training examples, and optimizing both models jointly. Our hallucinator can be incorporated into a variety of meta-learners and provides significant gains: up to a 6 point boost in classification accuracy when only a single training example is available, yielding state-of-the-art performance on the challenging ImageNet low-shot classification benchmark.