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50
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 521 (31 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 391 (48 self)
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This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and
An introduction to boosting and leveraging
 Advanced Lectures on Machine Learning, LNCS
, 2003
"... ..."
Support Vector Method for Novelty Detection
, 2000
"... Suppose you are given some dataset drawn from an underlying probability distributionPand you want to estimate a “simple ” subsetSof input space such that the probability that a test point drawn from P lies outside of Sequals some a priori specified between0and1. We propose a m ethod to approach this ..."
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Cited by 108 (4 self)
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Suppose you are given some dataset drawn from an underlying probability distributionPand you want to estimate a “simple ” subsetSof input space such that the probability that a test point drawn from P lies outside of Sequals some a priori specified between0and1. We propose a m ethod to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form offis 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. We provide a 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 data.
A Linear Programming Approach to Novelty Detection
, 2001
"... Novelty detection involves modeling the normal behaviour of a system hence enabling detection of any divergence from normality. It has potential applications in many areas such as detection of machine damage or highlighting abnormal features in medical data. One approach is to build a hypothesis ..."
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Cited by 69 (5 self)
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Novelty detection involves modeling the normal behaviour of a system hence enabling detection of any divergence from normality. It has potential applications in many areas such as detection of machine damage or highlighting abnormal features in medical data. One approach is to build a hypothesis estimating the support of the normal data i.e. constructing a function which is positive in the region where the data is located and negative elsewhere. Recently kernel methods have been proposed for estimating the support of a distribution and they have performed well in practice  training involves solution of a quadratic programming problem. In this paper we propose a simpler kernel method for estimating the support based on linear programming. The method is easy to implement and can learn large datasets rapidly. We demonstrate the method on medical and fault detection datasets. 1 Introduction. An important classification task is the ability to distinguish between new instance...
Constructing Boosting Algorithms from SVMs: An Application to Oneclass Classification
, 2002
"... ..."
A kernel method for the two sample problem
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 19
, 2007
"... We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert ..."
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Cited by 40 (13 self)
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We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg. a Banach space). We apply our twosample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.
A Review of Kernel Methods in Machine Learning
, 2006
"... We review recent methods for learning with positive definite kernels. All these methods formulate learning and estimation problems as linear tasks in a reproducing kernel Hilbert space (RKHS) associated with a kernel. We cover a wide range of methods, ranging from simple classifiers to sophisticate ..."
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Cited by 37 (3 self)
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We review recent methods for learning with positive definite kernels. All these methods formulate learning and estimation problems as linear tasks in a reproducing kernel Hilbert space (RKHS) associated with a kernel. We cover a wide range of methods, ranging from simple classifiers to sophisticated methods for estimation with structured data.
A SelfOrganising Network That Grows When Required
, 2002
"... The ability to grow extra nodes is a potentially useful facility for a selforganising neural network. A network that can add nodes into its map space can approximate the input space more accurately, and often more parsimoniously, than a network with predefined structure and size, such as the SelfO ..."
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Cited by 33 (5 self)
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The ability to grow extra nodes is a potentially useful facility for a selforganising neural network. A network that can add nodes into its map space can approximate the input space more accurately, and often more parsimoniously, than a network with predefined structure and size, such as the SelfOrganising Map. In addition, a growing network can deal with dynamic input distributions. Most of the growing networks that have been proposed in the literature add new nodes to support the node that has accumulated the highest error during previous iterations or to support topological structures. This usually means that new nodes are added only when the number of iterations is an integer multiple of some predefined constant,
SV Estimation of a Distribution's Support
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a 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 0 < 1. We propose an algorithm which appro ..."
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Cited by 28 (2 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a 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 0 < 1. We propose an algorithm which approaches 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 algorithm is a natural extension of the support vector algorithm to the case of unlabelled data.