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LIBSVM: a Library for Support Vector Machines
, 2001
"... LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1 ..."
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Cited by 6287 (82 self)
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LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1
A Comparison of Methods for Multiclass Support Vector Machines
 IEEE TRANS. NEURAL NETWORKS
, 2002
"... Support vector machines (SVMs) were originally designed for binary classification. How to effectively extend it for multiclass classification is still an ongoing research issue. Several methods have been proposed where typically we construct a multiclass classifier by combining several binary class ..."
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Cited by 935 (22 self)
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Support vector machines (SVMs) were originally designed for binary classification. How to effectively extend it for multiclass classification is still an ongoing research issue. Several methods have been proposed where typically we construct a multiclass classifier by combining several binary classifiers. Some authors also proposed methods that consider all classes at once. As it is computationally more expensive to solve multiclass problems, comparisons of these methods using largescale problems have not been seriously conducted. Especially for methods solving multiclass SVM in one step, a much larger optimization problem is required so up to now experiments are limited to small data sets. In this paper we give decomposition implementations for two such “alltogether” methods. We then compare their performance with three methods based on binary classifications: “oneagainstall,” “oneagainstone,” and directed acyclic graph SVM (DAGSVM). Our experiments indicate that the “oneagainstone” and DAG methods are more suitable for practical use than the other methods. Results also show that for large problems methods by considering all data at once in general need fewer support vectors.
A tutorial on support vector regression
, 2004
"... In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing ..."
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Cited by 828 (3 self)
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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.
SVMTorch: Support Vector Machines for LargeScale Regression Problems
 Journal of Machine Learning Research
, 2001
"... Support Vector Machines (SVMs) for regression problems are trained by solving a quadratic optimization problem which needs on the order of l 2 memory and time resources to solve, where l is the number of training examples. In this paper, we propose a decomposition algorithm, SVMTorch 1 , whic ..."
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Cited by 314 (10 self)
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Support Vector Machines (SVMs) for regression problems are trained by solving a quadratic optimization problem which needs on the order of l 2 memory and time resources to solve, where l is the number of training examples. In this paper, we propose a decomposition algorithm, SVMTorch 1 , which is similar to SVMLight proposed by Joachims (1999) for classification problems, but adapted to regression problems. With this algorithm, one can now efficiently solve largescale regression problems (more than 20000 examples). Comparisons with Nodelib, another publicly available SVM algorithm for largescale regression problems from Flake and Lawrence (2000) yielded significant time improvements. Finally, based on a recent paper from Lin (2000), we show that a convergence proof exists for our algorithm. 1. Introduction Vapnik (1995) has proposed a method to solve regression problems using support vector machines. It has yielded excellent performance on many regression and time ser...
Working set selection using second order information for training SVM
 Journal of Machine Learning Research
"... Working set selection is an important step in decomposition methods for training support vector machines (SVMs). This paper develops a new technique for working set selection in SMOtype decomposition methods. It uses second order information to achieve fast convergence. Theoretical properties such ..."
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Cited by 276 (11 self)
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Working set selection is an important step in decomposition methods for training support vector machines (SVMs). This paper develops a new technique for working set selection in SMOtype decomposition methods. It uses second order information to achieve fast convergence. Theoretical properties such as linear convergence are established. Experiments demonstrate that the proposed method is faster than existing selection methods using first order information.
Fast Kernel Classifiers With Online And Active Learning
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This ..."
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Cited by 153 (18 self)
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Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This contribution proposes an empirical answer. We first present an online SVM algorithm based on this premise. LASVM yields competitive misclassification rates after a single pass over the training examples, outspeeding stateoftheart SVM solvers. Then we show how active example selection can yield faster training, higher accuracies, and simpler models, using only a fraction of the training example labels.
A modified finite newton method for fast solution of large scale linear svms
 Journal of Machine Learning Research
, 2005
"... This paper develops a fast method for solving linear SVMs with L2 loss function that is suited for large scale data mining tasks such as text classification. This is done by modifying the finite Newton method of Mangasarian in several ways. Experiments indicate that the method is much faster than de ..."
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Cited by 109 (8 self)
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This paper develops a fast method for solving linear SVMs with L2 loss function that is suited for large scale data mining tasks such as text classification. This is done by modifying the finite Newton method of Mangasarian in several ways. Experiments indicate that the method is much faster than decomposition methods such as SVM light, SMO and BSVM (e.g., 4100 fold), especially when the number of examples is large. The paper also suggests ways of extending the method to other loss functions such as the modified Huber’s loss function and the L1 loss function, and also for solving ordinal regression.
Everything Old Is New Again: A Fresh Look at Historical Approaches
 in Machine Learning. PhD thesis, MIT
, 2002
"... 2 Everything Old Is New Again: A Fresh Look at Historical ..."
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Cited by 106 (7 self)
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2 Everything Old Is New Again: A Fresh Look at Historical
Incorporating Diversity in Active Learning with Support Vector Machines
 In ICML
, 2003
"... In many real world applications, active selection of training examples can significantly reduce the number of labelled training examples to learn a classification function. Different strategies in the field of support vector machines have been proposed that iteratively select a single new example fr ..."
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Cited by 104 (0 self)
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In many real world applications, active selection of training examples can significantly reduce the number of labelled training examples to learn a classification function. Different strategies in the field of support vector machines have been proposed that iteratively select a single new example from a set of unlabelled examples, query the corresponding class label and then perform retraining of the current classifier. However, to reduce computational time for training, it might be necessary to select batches of new training examples instead of single examples. Strategies for single examples can be extended straightforwardly to select batches by choosing the h> 1 examples that get the highest values for the individual selection criterion. We present a new approach that is especially designed to construct batches and incorporates a diversity measure. It has low computational requirements making it feasible for large scale problems with several thousands of examples. Experimental results indicate that this approach provides a faster method to attain a level of generalization accuracy in terms of the number of labelled examples. 1.
A Study on Sigmoid Kernels for SVM and the Training of nonPSD Kernels by SMOtype Methods
, 2003
"... The sigmoid kernel was quite popular for support vector machines due to its origin from neural networks. However, as the kernel matrix may not be positive semidefinite (PSD), it is not widely used and the behavior is unknown. In this paper, we analyze such nonPSD kernels through the point of view o ..."
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Cited by 91 (5 self)
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The sigmoid kernel was quite popular for support vector machines due to its origin from neural networks. However, as the kernel matrix may not be positive semidefinite (PSD), it is not widely used and the behavior is unknown. In this paper, we analyze such nonPSD kernels through the point of view of separability. Based on the investigation of parameters in different ranges, we show that for some parameters, the kernel matrix is conditionally positive definite (CPD), a property which explains its practical viability. Experiments are given to illustrate our analysis. Finally, we discuss how to solve the nonconvex dual problems by SMOtype decomposition methods. Suitable modifications for any symmetric nonPSD kernel matrices are proposed with convergence proofs.