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Proximal support vector machine classifiers
TLDR
Instead of a standard support vector machine (SVM) that classifies points by assigning them to one of two disjoint half-spaces, points are classified by assignment them to the closest of two parallel planes (in input or feature space) that are pushed apart as far as possible. Expand
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Feature Selection via Concave Minimization and Support Vector Machines
TLDR
Computational comparison is made between two feature selection approaches for nding a separating plane that discriminates between two point sets in an n-dimensional feature space that utilizes as few of the features (dimensions) as possible. Expand
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Multisurface proximal support vector machine classification via generalized eigenvalues
TLDR
A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Expand
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Nonlinear Programming
TLDR
We must show that A is closed for all k → x x , k → y y , where ( k A ∈ ) k y x is arbitrarily close to Z. Expand
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Multisurface method of pattern separation for medical diagnosis applied to breast cytology.
Multisurface pattern separation is a mathematical method for distinguishing between elements of two pattern sets. Each element of the pattern sets is comprised of various scalar observations. In thisExpand
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The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints
Optimality criteria form the foundations of mathematical programming both theoretically and computationally. In general, these criteria can be classified as either necessary or sufficient. Of course,Expand
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SSVM: A Smooth Support Vector Machine for Classification
TLDR
Smoothing methods, extensively used for solving important mathematical programming problems and applications, are applied here to generate an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel. Expand
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RSVM: Reduced Support Vector Machines
TLDR
We have proposed a Reduced Support Vector Machine (RSVM) Algorithm 3.1 that uses a randomly selected subset of the data that is typically 10% or less of the original dataset for its explicit evaluation. Expand
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Robust linear programming discrimination of two linearly inseparable sets
A single linear programming formulation is proposed which generates a plane that of minimizes an average sum of misclassified points belonging to two disjoint points sets in n-dimensional real space.Expand
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Lagrangian Support Vector Machines
TLDR
An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. Expand
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