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463
LIBSVM: A library for support vector machines,”
 ACM Transactions on Intelligent Systems and Technology,
, 2011
"... Abstract LIBSVM is a library for support vector machines (SVM). Its goal is to help users to easily use SVM as a tool. In this document, we present all its implementation details. For the use of LIBSVM, the README file included in the package and the LIBSVM FAQ provide the information. ..."
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Cited by 6496 (83 self)
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Abstract LIBSVM is a library for support vector machines (SVM). Its goal is to help users to easily use SVM as a tool. In this document, we present all its implementation details. For the use of LIBSVM, the README file included in the package and the LIBSVM FAQ provide the information.
Online Learning with Kernels
, 2003
"... Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little u ..."
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Cited by 2831 (123 self)
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Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little use of these methods in an online setting suitable for realtime applications. In this paper we consider online learning in a Reproducing Kernel Hilbert Space. By considering classical stochastic gradient descent within a feature space, and the use of some straightforward tricks, we develop simple and computationally efficient algorithms for a wide range of problems such as classification, regression, and novelty detection. In addition to allowing the exploitation of the kernel trick in an online setting, we examine the value of large margins for classification in the online setting with a drifting target. We derive worst case loss bounds and moreover we show the convergence of the hypothesis to the minimiser of the regularised risk functional. We present some experimental results that support the theory as well as illustrating the power of the new algorithms for online novelty detection. In addition
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.
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
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
Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2000
"... We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a marginbased binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class ..."
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Cited by 561 (20 self)
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We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a marginbased binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with errorcorrecting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms. The scheme and the corresponding bounds apply to many popular classification learning algorithms including supportvector machines, AdaBoost, regression, logistic regression and decisiontree algorithms. We also give a multiclass generalization error analysis for general output codes with AdaBoost as the binary learner. Experimental results with SVM and AdaBoost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms.
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 287 (12 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.
Incremental Online Learning in High Dimensions
 Neural Computation
, 2005
"... Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally e ..."
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Cited by 164 (19 self)
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Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally e#cient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic leaveoneout cross validation for learning without the need to memorize training data, iii) adjusts its weighting kernels based only on local information in order to minimize the danger of negative interference of incremental learning, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number of  possibly redundant  inputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and e#ciently operate in very high dimensional spaces.
MultiInstance Kernels
 In Proc. 19th International Conf. on Machine Learning
, 2002
"... Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attributevalue data. Only recently, research started investigating kernels for structured data. This paper considers kernels for multiinstance problems  a cla ..."
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Cited by 157 (3 self)
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Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attributevalue data. Only recently, research started investigating kernels for structured data. This paper considers kernels for multiinstance problems  a class of concepts on individuals represented by sets. The main result of this paper is a kernel on multiinstance data that can be shown to separate positive and negative sets under natural assumptions. This kernel compares favorably with state of the art multiinstance learning algorithms in an empirical study. Finally, we give some concluding remarks and propose future work that might further improve the results.
An introduction to boosting and leveraging
 Advanced Lectures on Machine Learning, LNCS
, 2003
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