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117
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 3393 (12 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.
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 865 (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.
An introduction to kernelbased learning algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2001
"... This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and ..."
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Cited by 598 (55 self)
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This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and
Learning with Labeled and Unlabeled Data
, 2001
"... In this paper, on the one hand, we aim to give a review on literature dealing with the problem of supervised learning aided by additional unlabeled data. On the other hand, being a part of the author's first year PhD report, the paper serves as a frame to bundle related work by the author as we ..."
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Cited by 202 (3 self)
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In this paper, on the one hand, we aim to give a review on literature dealing with the problem of supervised learning aided by additional unlabeled data. On the other hand, being a part of the author's first year PhD report, the paper serves as a frame to bundle related work by the author as well as numerous suggestions for potential future work. Therefore, this work contains more speculative and partly subjective material than the reader might expect from a literature review. We give a rigorous definition of the problem and relate it to supervised and unsupervised learning. The crucial role of prior knowledge is put forward, and we discuss the important notion of inputdependent regularization. We postulate a number of baseline methods, being algorithms or algorithmic schemes which can more or less straightforwardly be applied to the problem, without the need for genuinely new concepts. However, some of them might serve as basis for a genuine method. In the literature revi...
Training Invariant Support Vector Machines
, 2002
"... Practical experience has shown that in order to obtain the best possible performance, prior knowledge about invariances of a classification problem at hand ought to be incorporated into the training procedure. We describe and review all known methods for doing so in support vector machines, provide ..."
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Cited by 186 (16 self)
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Practical experience has shown that in order to obtain the best possible performance, prior knowledge about invariances of a classification problem at hand ought to be incorporated into the training procedure. We describe and review all known methods for doing so in support vector machines, provide experimental results, and discuss their respective merits. One of the significant new results reported in this work is our recent achievement of the lowest reported test error on the wellknown MNIST digit recognition benchmark task, with SVM training times that are also significantly faster than previous SVM methods.
The connection between regularization operators and support vector kernels
, 1998
"... In this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green’s Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, ..."
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Cited by 175 (40 self)
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In this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green’s Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, the paper provides an analysis of currently used support vector kernels in the view of regularization theory and corresponding operators associated with the classes of both polynomial kernels and translation invariant kernels. The latter are also analyzed on periodical domains. As a byproduct we show that a large number of radial basis functions, namely conditionally positive definite
Engineering Support Vector Machine Kernels That Recognize Translation Initiation Sites
, 2000
"... Motivation: In order to extract protein sequences from nucleotide sequences, it is an important step to recognize points at which regions start that code for proteins. These points are called translation initiation sites (TIS). Results: The task of finding TIS can be modeled as a classification pro ..."
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Cited by 133 (14 self)
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Motivation: In order to extract protein sequences from nucleotide sequences, it is an important step to recognize points at which regions start that code for proteins. These points are called translation initiation sites (TIS). Results: The task of finding TIS can be modeled as a classification problem. We demonstrate the applicability of support vector machines (SVMs) for this task, and show how to incorporate prior biological knowledge by engineering an appropriate kernel function. With the described techniques the recognition performance can be improved by 26% over leading existing approaches. We provide evidence that existing related methods (e.g. ESTScan) could profit from advanced TIS recognition.
Input Space Versus Feature Space in KernelBased Methods
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 1999
"... This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature spac ..."
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Cited by 130 (3 self)
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This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods. Following this, we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel, using the example of the class of inhomogeneous polynomial kernels, which are often used in SV pattern recognition. We then discuss the connection between feature space and input space by dealing with the question of how one can, given some vector in feature space, find a preimage (exact or approximate) in input space. We describe algorithms to tackle this issue, and show their utility in two applications of kernel methods. First, we use it to reduce the computational complexity of SV decision functions; second, we combine it with the Kernel PCA algorithm, thereby constructing a nonlinear statistical denoising technique which is shown to perform well on realworld data.
A novel transductive SVM for the semisupervised classification of remote sensing images
 IEEE Trans. Geoscience and Remote Sensing
, 2006
"... Abstract—This paper introduces a semisupervised classification method that exploits both labeled and unlabeled samples for addressing illposed problems with support vector machines (SVMs). The method is based on recent developments in statistical learning theory concerning transductive inference an ..."
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Cited by 64 (9 self)
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Abstract—This paper introduces a semisupervised classification method that exploits both labeled and unlabeled samples for addressing illposed problems with support vector machines (SVMs). The method is based on recent developments in statistical learning theory concerning transductive inference and in particular transductive SVMs (TSVMs). TSVMs exploit specific iterative algorithms which gradually search a reliable separating hyperplane (in the kernel space) with a transductive process that incorporates both labeled and unlabeled samples in the training phase. Based on an analysis of the properties of the TSVMs presented in the literature, a novel modified TSVM classifier designed for addressing illposed remotesensing problems is proposed. In particular, the proposed technique: 1) is based on a novel transductive procedure that exploits a weighting strategy for unlabeled patterns, based on a timedependent criterion; 2) is able to mitigate the effects of suboptimal model selection (which is unavoidable in the presence of smallsize training sets); and 3) can address multiclass cases. Experimental results confirm the effectiveness of the proposed method on a set of illposed remotesensing classification problems representing different operative conditions. Index Terms—Illposed problems, labeled and unlabeled patterns, machine learning, remote sensing, semisupervised classification, support vector machines (SVMs), transductive inference. I.
Shrinking the Tube: A New Support Vector Regression Algorithm
, 1999
"... A new algorithm for Support Vector regression is described. For a priori chosen , it automatically adjusts a flexible tube of minimal radius to the data such that at most a fraction of the data points lie outside. Moreover, it is shown how to use parametric tube shapes with nonconstant radius. ..."
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Cited by 57 (5 self)
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A new algorithm for Support Vector regression is described. For a priori chosen , it automatically adjusts a flexible tube of minimal radius to the data such that at most a fraction of the data points lie outside. Moreover, it is shown how to use parametric tube shapes with nonconstant radius. The algorithm is analysed theoretically and experimentally.