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Proximal support vector machine classifiers
TLDR
Computational results on publicly available datasets indicate that the proposed proximal SVM classifier has comparable test set correctness to that of standard S VM classifiers, but with considerably faster computational time that can be an order of magnitude faster.
Feature Selection via Concave Minimization and Support Vector Machines
TLDR
Numerical tests on 6 public data sets show that classi ers trained by the concave minimization approach and those trained by a support vector machine have comparable 10fold cross-validation correctness.
Multisurface proximal support vector machine classification via generalized eigenvalues
TLDR
Tests on simple examples as well as on a number of public data sets show the advantages of the proposed approach in both computation time and test set correctness.
Multisurface method of pattern separation for medical diagnosis applied to breast cytology.
TLDR
The diagnosis of breast cytology is used to demonstrate the applicability ofMultisurface pattern separation to medical diagnosis and decision making and it is found that this mathematical method is applicable to other medical diagnostic and decision-making problems.
SSVM: A Smooth Support Vector Machine for Classification
TLDR
Smoothing methods are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel, which converges globally and quadratically.
Nonlinear Programming
TLDR
It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Robust linear programming discrimination of two linearly inseparable sets
TLDR
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, without the imposition of extraneous normalization constraints that inevitably fail to handle certain cases.
RSVM: Reduced Support Vector Machines
TLDR
Computational results indicate that test set correctness for the reduced support vector machine (RSVM), with a nonlinear separating surface that depends on a small randomly selected portion of the dataset, is better than that of a conventional support vectors machine (SVM) with aNonlinear surface that explicitly depends on the entire dataset, and much better than a conventional SVM using a small random sample of the data.
Lagrangian Support Vector Machines
An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. This leads to the minimization of an unconstrained
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