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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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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
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 506 (0 self)
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the family of radial basis kernels. It can also be used to define kernels in the form of joint Gibbs probability distributions. Kernels can be built from hidden Markov random elds, generalized regular expressions, pairHMMs, or ANOVA decompositions. Uses of the method lead to open problems involving
Improving Support Vector Machine Classifiers by Modifying Kernel Functions
 NEURAL NETWORKS
, 1999
"... We propose a method of modifying a kernel function to improve the performance of a support vector machine classifier. This is based on the Riemannian geometrical structure induced by the kernel function. The idea is to enlarge the spatial resolution around the separating boundary surface by a con ..."
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Cited by 89 (3 self)
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conformal mapping such that the separability between classes is increased. Examples are given specifically for modifying Gaussian Radial Basis Function kernels. Simulation results for both artificial and real data show remarkable improvement of generalization errors, supporting our idea.
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 505 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs
Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1997
"... The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights an ..."
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Cited by 183 (13 self)
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The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights
A training algorithm for optimal margin classifiers
 PROCEEDINGS OF THE 5TH ANNUAL ACM WORKSHOP ON COMPUTATIONAL LEARNING THEORY
, 1992
"... A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjust ..."
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Cited by 1865 (43 self)
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A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vect ..."
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Cited by 966 (5 self)
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functions than a comparable SVM while offering a number of additional advantages. These include the benefits of probabilistic predictions, automatic estimation of `nuisance’ parameters, and the facility to utilise arbitrary basis functions (e.g. non`Mercer’ kernels). We detail the Bayesian framework
Training Support Vector Machines: an Application to Face Detection
, 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
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Cited by 727 (1 self)
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We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision
The "Independent Components" of Natural Scenes are Edge Filters
, 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
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Cited by 617 (29 self)
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distributions. We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zerophase whitening filters (ZCA). The ICA filters have more sparsely distributed (kurtotic) outputs on natural scenes. They also
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 476 (46 self)
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stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LSSVM classifiers with linear, polynomial and radial basis function
Results 1  10
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6,040