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55
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 2356 (11 self)
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The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.
Large margin dags for multiclass classification
 Advances in Neural Information Processing Systems 12
, 2000
"... We present a new learning architecture: the Decision Directed Acyclic Graph (DDAG), which is used to combine many twoclass classifiers into a multiclass classifier. For anclass problem, the DDAG contains � classifiers, one for each pair of classes. We present a VC analysis of the case when the nod ..."
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Cited by 267 (1 self)
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We present a new learning architecture: the Decision Directed Acyclic Graph (DDAG), which is used to combine many twoclass classifiers into a multiclass classifier. For anclass problem, the DDAG contains � classifiers, one for each pair of classes. We present a VC analysis of the case when the node classifiers are hyperplanes; the resulting bound on the test error depends on and on the margin achieved at the nodes, but not on the dimension of the space. This motivates an algorithm, DAGSVM, which operates in a kernelinduced feature space and uses twoclass maximal margin hyperplanes at each decisionnode of the DDAG. The DAGSVM is substantially faster to train and evaluate than either the standard algorithm or Max Wins, while maintaining comparable accuracy to both of these algorithms. 1
Improving the Accuracy and Speed of Support Vector Machines
 Advances in Neural Information Processing Systems 9
, 1997
"... Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion for illposed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs ..."
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Cited by 145 (20 self)
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Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion for illposed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs are of increasing interest. In this paper we combine two such techniques on a pattern recognition problem. The method for improving generalization performance (the "virtual support vector" method) does so by incorporating known invariances of the problem. This method achieves a drop in the error rate on 10,000 NIST test digit images of 1.4% to 1.0%. The method for improving the speed (the "reduced set" method) does so by approximating the support vector decision surface. We apply this method to achieve a factor of fifty speedup in test phase over the virtual support vector machine. The combined approach yields a machine which is both 22 times faster than the original machine, and which has ...
Use of the ZeroNorm With Linear Models and Kernel Methods
, 2002
"... We explore the use of the socalled zeronorm of the parameters of linear models in learning. ..."
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Cited by 116 (3 self)
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We explore the use of the socalled zeronorm of the parameters of linear models in learning.
Support Vector Machines for Classification in Nonstandard Situations
 MACHINE LEARNING
, 2000
"... The majority of classification algorithms are developed for the standard situation in which it is assumed that the examples in the training set come from the same distribution as that of the target population, and that the cost of misclassification into di#erent classes are the same. However, these ..."
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Cited by 76 (15 self)
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The majority of classification algorithms are developed for the standard situation in which it is assumed that the examples in the training set come from the same distribution as that of the target population, and that the cost of misclassification into di#erent classes are the same. However, these assumptions are often violated in real world settings. For some classification methods, this can often be taken care of simply with a change of threshold; for others, additional e#ort is required. In this paper, we explain why the standard support vector machine is not suitable for the nonstandard situation, and introduce a simple procedure for adapting the support vector machine methodology to the nonstandard situation. Theoretical justification for the procedure is provided. Simulation study illustrates that the modified support vector machine significantly improves upon the standard support vector machine in the nonstandard situation. The computational load of the proposed procedure is th...
On a Kernelbased Method for Pattern Recognition, Regression, Approximation, and Operator Inversion
, 1997
"... We present a Kernelbased framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridgeregression, Support Vector methods and regression by Smoothing Kernels are included as special cases. We will show connection ..."
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Cited by 76 (23 self)
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We present a Kernelbased framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridgeregression, Support Vector methods and regression by Smoothing Kernels are included as special cases. We will show connections between the costfunction and some properties up to now believed to apply to Support Vector Machines only. The optimal solution of all the problems described above can be found by solving a simple quadratic programming problem. The paper closes with a proof of the equivalence between Support Vector kernels and Greene's functions of regularization operators.
Feature Selection for Support Vector Machines by Means of Genetic Algorithms
, 2002
"... The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance, e.g. in bioinformatics. Genetic Algorithms (GAs) offer a natural way to solve this problem. In this paper we present a special Genetic Algorithm, which especially takes into accoun ..."
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Cited by 51 (1 self)
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The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance, e.g. in bioinformatics. Genetic Algorithms (GAs) offer a natural way to solve this problem. In this paper we present a special Genetic Algorithm, which especially takes into account the existing bounds on the generalization error for Support Vector Machines (SVMs). This new approach is compared to the traditional method of performing crossvalidation and to other existing algorithms for feature selection.