Polyhedral separability through successive LP

DOI10.1023/A:1013649822153zbMath1049.90039OpenAlexW1481810791WikidataQ62473108 ScholiaQ62473108MaRDI QIDQ5959910

Annabella Astorino, Manlio Gaudioso

Publication date: 11 April 2002

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1013649822153

zbMATH Keywords

Classification, separability, machine learning

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08)

Related Items (30)

On the problem polyhedral separability: a numerical solution ⋮ A characterization of 2-threshold functions via pairs of prime segments ⋮ A fixed-center spherical separation algorithm with kernel transformations for classification problems ⋮ On numerical solving the spherical separability problem ⋮ Mathematical diagnostics via nonsmooth analysis ⋮ Data pre-classification and the separation law for closed bounded convex sets ⋮ Ellipsoidal separation for classification problems ⋮ Max–min separability ⋮ DC models for spherical separation ⋮ A polyhedral conic functions based classification method for noisy data ⋮ Margin maximization in spherical separation ⋮ An aggregate deformation homotopy method for min-max-min problems with max-min constraints ⋮ An incremental piecewise linear classifier based on polyhedral conic separation ⋮ Efficient MIP techniques for computing the relaxation complexity ⋮ A novel piecewise linear classifier based on polyhedral conic and max-min separabilities ⋮ An approach to classification based on separation of sets by means of several ellipsoids ⋮ An effective method to determine whether a point is within a convex hull and its generalized convex polyhedron classifier ⋮ A DC optimization-based clustering technique for edge detection ⋮ Accurately learning from few examples with a polyhedral classifier ⋮ Optimization approaches to supervised classification ⋮ A constraint generation algorithm for large scale linear programs using multiple-points separation ⋮ A new method based on the proximal bundle idea and gradient sampling technique for minimizing nonsmooth convex functions ⋮ The method of virtual experts in mathematical diagnostics ⋮ Classification through incremental max-min separability ⋮ Separation of convex sets by Clarke subdifferential ⋮ Clustering based polyhedral conic functions algorithm in classification ⋮ Separation via polyhedral conic functions ⋮ Support vector machine polyhedral separability in semisupervised learning ⋮ Polyhedral separation via difference of convex (DC) programming ⋮ On the solution of min-sum-min problems

Uses Software

• SVMlight

Cites Work

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• On the complexity of polyhedral separability
• Arbitrary-norm separating plane
• Bilinear separation of two sets in \(n\)-space
• Misclassification minimization
• Feature minimization within decision trees
• Improved generalization via tolerant training
• Hybrid misclassification minimization
• Mathematical Programming Methods of Pattern Classification
• Mathematical Programming in Neural Networks
• A Parametric Optimization Method for Machine Learning
• Breast Cancer Diagnosis and Prognosis Via Linear Programming
• Massive data discrimination via linear support vector machines
• Linear and Nonlinear Separation of Patterns by Linear Programming
• Multisurface method of pattern separation

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