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The Nature of Statistical Learning Theory
, 1995
"... Abstract—Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on ..."
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Cited by 9218 (28 self)
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Abstract—Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the developed theory were proposed. This made statistical learning theory not only a tool for the theoretical analysis but also a tool for creating practical algorithms for estimating multidimensional functions. This article presents a very general overview of statistical learning theory including both theoretical and algorithmic aspects of the theory. The goal of this overview is to demonstrate how the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems.
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 3578 (62 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 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.
Shape Matching and Object Recognition Using Shape Contexts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform ..."
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Cited by 1274 (19 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape con texts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; reg ularized thin plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning trans form. We treat recognition in a nearestneighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1073 (71 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5pixel products in 16x16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
Boosting the margin: A new explanation for the effectiveness of voting methods
 In Proceedings International Conference on Machine Learning
, 1997
"... Abstract. One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show ..."
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Cited by 733 (52 self)
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Abstract. One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik’s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the biasvariance decomposition. 1
Gene selection for cancer classification using support vector machines
 Machine Learning
"... Abstract. DNA microarrays now permit scientists to screen thousands of genes simultaneously and determine whether those genes are active, hyperactive or silent in normal or cancerous tissue. Because these new microarray devices generate bewildering amounts of raw data, new analytical methods must ..."
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Cited by 698 (24 self)
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Abstract. DNA microarrays now permit scientists to screen thousands of genes simultaneously and determine whether those genes are active, hyperactive or silent in normal or cancerous tissue. Because these new microarray devices generate bewildering amounts of raw data, new analytical methods must be developed to sort out whether cancer tissues have distinctive signatures of gene expression over normal tissues or other types of cancer tissues. In this paper, we address the problem of selection of a small subset of genes from broad patterns of gene expression data, recorded on DNA microarrays. Using available training examples from cancer and normal patients, we build a classifier suitable for genetic diagnosis, as well as drug discovery. Previous attempts to address this problem select genes with correlation techniques. We propose a new method of gene selection utilizing Support Vector Machine methods based on Recursive Feature Elimination (RFE). We demonstrate experimentally that the genes selected by our techniques yield better classification performance and are biologically relevant to cancer. In contrast with the baseline method, our method eliminates gene redundancy automatically and yields better and more compact gene subsets. In patients with leukemia our method discovered 2 genes that yield zero leaveoneout error, while 64 genes are necessary for the baseline method to get the best result (one leaveoneout error). In the colon cancer database, using only 4 genes our method is 98 % accurate, while the baseline method is only 86 % accurate.
A ReExamination of Text Categorization Methods
, 1999
"... This paper reports a controlled study with statistical significance tests on five text categorization methods: the Support Vector Machines (SVM), a kNearest Neighbor (kNN) classifier, a neural network (NNet) approach, the Linear Leastsquares Fit (LLSF) mapping and a NaiveBayes (NB) classifier. We f ..."
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Cited by 662 (19 self)
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This paper reports a controlled study with statistical significance tests on five text categorization methods: the Support Vector Machines (SVM), a kNearest Neighbor (kNN) classifier, a neural network (NNet) approach, the Linear Leastsquares Fit (LLSF) mapping and a NaiveBayes (NB) classifier. We focus on the robustness of these methods in dealing with a skewed category distribution, and their performance as function of the trainingset category frequency. Our results show that SVM, kNN and LLSF significantly outperform NNet and NB when the number of positive training instances per category are small (less than ten), and that all the methods perform comparably when the categories are sufficiently common (over 300 instances).
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 590 (15 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.