Fundamental Issues in Support Vector Machines

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This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful … continued below

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iii, 48 pages

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McWhorter, Samuel P. May 2014.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by the UNT Libraries to the UNT Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 94 times. More information about this dissertation can be viewed below.

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  • McWhorter, Samuel P.

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Description

This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its final section presents an algorithm by Dr. Kallman (preprint), based on earlier Russian work by B.F. Mitchell, V.F Demyanov, and V.N. Malozemov, and proves its convergence. The section also discusses briefly architectural features of the algorithm expected to result in practical speed increases.

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iii, 48 pages

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UNT Theses and Dissertations

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  • May 2014

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  • March 8, 2015, 5:44 p.m.

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  • Nov. 16, 2016, 1:14 p.m.

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McWhorter, Samuel P. Fundamental Issues in Support Vector Machines, dissertation, May 2014; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc500155/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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