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New Support Vector Algorithms
, 2000
"... this article with the regression case. To explain this, we will introduce a suitable definition of a margin that is maximized in both cases ..."
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Cited by 322 (45 self)
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this article with the regression case. To explain this, we will introduce a suitable definition of a margin that is maximized in both cases
A Kernel Approach for Learning From Almost Orthogonal Patterns
, 2002
"... In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well. We propose and test several methods for dealing with this problem by reducing the ..."
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Cited by 30 (4 self)
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In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well. We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine.
Wadge Degrees of Infinitary Rational Relations
, 2008
"... We show that, from the topological point of view, 2tape Büchi automata have the same accepting power as Turing machines equipped with a Büchi acceptance condition. The Borel and the Wadge hierarchies of the class RATω of infinitary rational relations accepted by 2tape Büchi automata are equal to t ..."
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Cited by 4 (4 self)
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We show that, from the topological point of view, 2tape Büchi automata have the same accepting power as Turing machines equipped with a Büchi acceptance condition. The Borel and the Wadge hierarchies of the class RATω of infinitary rational relations accepted by 2tape Büchi automata are equal to the Borel and the Wadge hierarchies of ωlanguages accepted by realtime Büchi 1counter automata or by Büchi Turing machines. In particular, for every non null recursive ordinal α, there exist some Σ 0 αcomplete and some Π 0 αcomplete infinitary rational relations. And the supremum of the set of Borel ranks of infinitary rational relations is an ordinal γ 1 2 which is strictly greater than the first non recursive ordinal ω CK 1. This very surprising result gives answers to questions of Simonnet [Sim92] and of Lescow and Thomas [Tho88, LT94].
Variations of the twospiral task
, 2007
"... The twospiral task is a wellknown benchmark for binary classification. The data consist of points on two intertwined spirals which cannot be linearly separated. This article reviews how this task and some of its variations have significantly inspired the development of several important methods in ..."
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The twospiral task is a wellknown benchmark for binary classification. The data consist of points on two intertwined spirals which cannot be linearly separated. This article reviews how this task and some of its variations have significantly inspired the development of several important methods in the history of artificial neural networks. The twospiral task became popular for several different reasons: 1) It was regarded as extremely challenging; 2) It belonged to a suite of standard benchmark tasks; 3) It had visual appeal and was convenient to use in pilot studies. The article also presents an example which demonstrates how small variations of the twospiral task such as relative rotations of the two spirals can lead to qualitatively different generalisation results.
Support Vector Machines Based Filtering of Lidar Data: A Grid Based Method
"... This study introduces a method for filtering lidar data based on a Support Vector Machines (SVMs) classification method. Four study areas with different sensors and scene characteristics were investigated. First, the Digital Surface Model (DSM) was generated for the first and last pulses and then th ..."
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This study introduces a method for filtering lidar data based on a Support Vector Machines (SVMs) classification method. Four study areas with different sensors and scene characteristics were investigated. First, the Digital Surface Model (DSM) was generated for the first and last pulses and then the differences between the first and last pulses (FPLP) were computed. A total of 25 uncorrelated feature attributes have been generated from the aerial images, the lidar intensity image, DSM and FPLP. The generated attributes were applied in seven separate groups which include those from: Red, Green and Blue bands of the aerial image; Intensity/IR image; DSM; FPLP and the Total group of attributes. Finally, SVMs were used to automatically classify buildings, trees, roads and ground from aerial images, lidar data and the generated attributes, with the most accurate average classifications of 95% being achieved. The Gaussian Radius Basis Function (RBF) kernel model was applied to find the separating hyperplane for the SVMs classification. A binary image was then generated by converting the digital numbers of roads and grass to one while the digital numbers of buildings and trees were converted to zeros and all DSM’s pixels which correspond to a pixel value of one in the binary image were interpolated into a