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13
A.: Parametric local metric learning for nearest neighbor classification
 NIPS 2012 ECML/PKDD 2013 MACHINE LEARNING LAB 9/19/13 31/34 ECML/PKDD 2013
"... 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 p ..."
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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 largescale 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. 1
Image set classification using holistic multiple order statistics features and localized multikernel metric learning
 In ICCV
, 2013
"... This paper presents a new approach for image set classification, where each training and testing example contains a set of image instances of an object captured from varying viewpoints or under varying illuminations. While a number of image set classification methods have been proposed in recent ye ..."
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This paper presents a new approach for image set classification, where each training and testing example contains a set of image instances of an object captured from varying viewpoints or under varying illuminations. While a number of image set classification methods have been proposed in recent years, most of them model each image set as a single linear subspace or mixture of linear subspaces, which may lose some discriminative information for classification. To address this, we propose exploring multiple order statistics as features of image sets, and develop a localized multikernel metric learning (LMKML) algorithm to effectively combine different order statistics information for classification. Our method achieves the stateoftheart performance on four widely used databases including the Honda/UCSD, CMU Mobo, and Youtube face datasets, and the ETH80 object dataset. 1.
GenDeR: A Generic Diversified Ranking Algorithm
"... Diversified ranking is a fundamental task in machine learning. It is broadly applicable in many real world problems, e.g., information retrieval, team assembling, product search, etc. In this paper, we consider a generic setting where we aim to diversify the topk ranking list based on an arbitrary ..."
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Cited by 8 (0 self)
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Diversified ranking is a fundamental task in machine learning. It is broadly applicable in many real world problems, e.g., information retrieval, team assembling, product search, etc. In this paper, we consider a generic setting where we aim to diversify the topk ranking list based on an arbitrary relevance function and an arbitrary similarity function among all the examples. We formulate it as an optimization problem and show that in general it is NPhard. Then, we show that for a large volume of the parameter space, the proposed objective function enjoys the diminishing returns property, which enables us to design a scalable, greedy algorithm to find the (1 − 1/e) nearoptimal solution. Experimental results on real data sets demonstrate the effectiveness of the proposed algorithm. 1
Informationtheoretic Semisupervised Metric Learning via Entropy Regularization
"... We propose a general informationtheoretic approach called SERAPH (SEmisupervised metRic leArning Paradigm with Hypersparsity) for metric learning that does not rely upon the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize the entropy of that probabi ..."
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Cited by 5 (0 self)
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We propose a general informationtheoretic approach called SERAPH (SEmisupervised metRic leArning Paradigm with Hypersparsity) for metric learning that does not rely upon the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize the entropy of that probability on labeled data and minimize it on unlabeled data following entropy regularization, which allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Furthermore, SERAPH is regularized by encouraging a lowrank projection induced from the metric. The optimization of SERAPH is solved efficiently and stably by an EMlike scheme with the analytical EStep and convex MStep. Experiments demonstrate that SERAPH compares favorably with many wellknown global and local metric learning methods. 1.
Learning neighborhoods for metric learning
 In ECMLPKDD
, 2012
"... Abstract. Metric learning methods have been shown to perform well on different learning tasks. Many of them rely on target neighborhood relationships that are computed in the original feature space and remain fixed throughout learning. As a result, the learned metric reflects the original neighborho ..."
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Abstract. Metric learning methods have been shown to perform well on different learning tasks. Many of them rely on target neighborhood relationships that are computed in the original feature space and remain fixed throughout learning. As a result, the learned metric reflects the original neighborhood relations. We propose a novel formulation of the metric learning problem in which, in addition to the metric, the target neighborhood relations are also learned in a twostep iterative approach. The new formulation can be seen as a generalization of many existing metric learning methods. The formulation includes a target neighbor assignment rule that assigns different numbers of neighbors to instances according to their quality; ‘high quality ’ instances get more neighbors. We experiment with two of its instantiations that correspond to the metric learning algorithms LMNN and MCML and compare it to other metric learning methods on a number of datasets. The experimental results show stateoftheart performance and provide evidence that learning the neighborhood relations does improve predictive performance.
TwoStage Metric Learning
"... In this paper, we present a novel twostage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the asso ..."
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In this paper, we present a novel twostage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical manifold. This induces in the input data space a new family of distance metric with unique properties. Unlike kernelized metric learning, we do not require the similarity measure to be positive semidefinite. Moreover, it can also be interpreted as a local metric learning algorithm with well defined distance approximation. We evaluate its performance on a number of datasets. It outperforms significantly other metric learning methods and SVM. 1.
A Fast Clustering Algorithm for Data with a Few Labeled Instances
"... The diameter of a cluster is the maximum intracluster distance between pairs of instances within the same cluster, and the split of a cluster is the minimum distance between instances within the cluster and instances outside the cluster. Given a few labeled instances, this paper includes two aspect ..."
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The diameter of a cluster is the maximum intracluster distance between pairs of instances within the same cluster, and the split of a cluster is the minimum distance between instances within the cluster and instances outside the cluster. Given a few labeled instances, this paper includes two aspects. First, we present a simple and fast clustering algorithm with the following property: if the ratio of the minimum split to the maximum diameter (RSD) of the optimal solution is greater than one, the algorithm returns optimal solutions for three clustering criteria. Second, we study the metric learning problem: learn a distance metric to make the RSD as large as possible. Compared with existing metric learning algorithms, one of our metric learning algorithms is computationally efficient: it is a linear programming model rather than a semidefinite programming model used by most of existing algorithms. We demonstrate empirically that the supervision and the learned metric can improve the clustering quality.
Beyond Mahalanobis Metric: CayleyKlein Metric Learning
"... CayleyKlein metric is a kind of nonEuclidean metric suitable for projective space. In this paper, we introduce it into the computer vision community as a powerful metric and an alternative to the widely studied Mahalanobis metric. We show that besides its good characteristic in nonEuclidean spac ..."
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CayleyKlein metric is a kind of nonEuclidean metric suitable for projective space. In this paper, we introduce it into the computer vision community as a powerful metric and an alternative to the widely studied Mahalanobis metric. We show that besides its good characteristic in nonEuclidean space, it is a generalization of Mahalanobis metric in some specific cases. Furthermore, as many Mahalanobis metric learning, we give two kinds of CayleyKlein metric learning methods: MMC CayleyKlein metric learning and LMNN CayleyKlein metric learning. Experiments have shown the superiority of CayleyKlein metric over Mahalanobis ones and the effectiveness of our CayleyKlein metric learning methods. 1.
1A Kernel Classification Framework for Metric Learning
"... Abstract—Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several stateoftheart metric learning methods, such as large ..."
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Abstract—Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several stateoftheart metric learning methods, such as large margin nearest neighbor (LMNN) and information theoretic metric learning (ITML), into a kernel classification framework. First, doublets and triplets are constructed from the training samples, and a family of degree2 polynomial kernel functions are proposed for pairs of doublets or triplets. Then, a kernel classification framework is established to generalize many popular metric learning methods such as LMNN and ITML. The proposed framework can also suggest new metric learning methods, which can be efficiently implemented, interestingly, by using the standard support vector machine (SVM) solvers. Two novel metric learning methods, namely doubletSVM and tripletSVM, are then developed under the proposed framework. Experimental results show that doubletSVM and tripletSVM achieve competitive classification accuracies with stateoftheart metric learning methods but with significantly less training time. Index Terms—Metric learning, support vector machine, nearest neighbor, kernel method, polynomial kernel. I.