Now showing items 21-40 of 46

    • Massive Data Classification via Unconstrained Support Vector Machines 

      Thompson, Michael; Mangasarian, Olvi (2006)
      A highly accurate algorithm, based on support vector machines formulated as linear programs [13, 1], is proposed here as a completely unconstrained minimization problem [15]. Combined with a chunking procedure [2] this ...
    • Multiple Instance Classification via Successive Linear Programming 

      Wild, Edward; Mangasarian, Olvi (2005)
      The multiple instance classification problem [6,2,12] is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite dimensional (noninteger) real space subject to linear and bilinear ...
    • A Newton Method for Linear Programming 

      Mangasarian, Olvi (2002)
      A fast Newton method is proposed for solving linear programs with a very large ( 106) number of constraints and a moderate ( 102) number of variables. Such linear programs occur in data mining and machine learning. ...
    • Nonlinear Knowledge in Kernel Approximation 

      Wild, Edward; Mangasarian, Olvi (2006)
      Prior knowledge over arbitrary general sets is incorporated into nonlinear kernel approximation problems in the form of linear constraints in a linear program. The key tool in this incorporation is a theorem of the ...
    • Nonlinear Knowledge-Based Classification 

      Wild, Edward; Mangasarian, Olvi (2006)
      Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification problems as linear constraints in a linear program. The key tool in this incorporation is a theorem of the alternative for ...
    • An optimization approach for radiosurgery treatment planning 

      Shepard, David; Lim, Jinho; Ferris, Michael (2001-11-06)
      We outline a new approach for radiosurgery treatment planning, based on solving a series of optimization problems. We consider a speci c treat- ment planning problem for a specialized device known as the Gamma Knife, ...
    • Optimization of Gamma Knife Radiosurgery 

      Shepard, David; Ferris, Michael (2000)
      The Gamma Knife is a highly specialized treatment unit that pro- vides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded ...
    • A Practical Approach to Sample-path Simulation Optimization 

      Munson, Todd; Ferris, Michael (2000)
      We propose solving continuous parametric simulation optimizations using a deterministic nonlinear optimiza- tion algorithm and sample-path simulations. The op- timization problem is written in a modeling language with ...
    • Primal-Dual Bilinear Programming Solution of the Absolute Value Equation 

      Mangasarian, Olvi (2011)
      We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax ? |x| = b, where A is an n � n square matrix. The algorithm, which makes no ...
    • Privacy-Preserving Classification of Horizontally Partitioned Data via Random Kernels 

      Wild, E; Mangasarian, Olvi (2007)
      We propose a novel privacy-preserving nonlinear support vector machine (SVM) classifier for a data matrix A whose columns represent input space features and whose individual rows are divided into groups of rows. Each ...
    • Privacy-Preserving Classification of Vertically Partitioned Data via Random Kernels 

      Fung, Glenn; Wild, Edward; Mangasarian, Olvi (2007)
      We propose a novel privacy-preserving support vector machine (SVM) classifier for a data matrix A whose input feature columns are divided into groups belonging to different entities. Each entity is unwilling to share its ...
    • Privacy-Preserving Horizontally Partitioned Linear Programs 

      Mangasarian, Olvi (2010)
      We propose a simple privacy-preserving reformulation of a linear program whose equality constraint matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side vector are ...
    • Privacy-Preserving Linear and Nonlinear Approximation via Linear Programming 

      Mangasarian, Olvi; Fung, Glenn (2011)
      We propose a novel privacy-preserving random kernel approximation based on a data matrix A ? Rm�n whose rows are divided into privately owned blocks. Each block of rows belongs to a different entity that is unwilling to ...
    • Privacy-Preserving Random Kernel Classification of Checkerboard Partitioned Data 

      Wild, Edward; Mangasarian, Olvi (2008)
      We propose a privacy-preserving support vector machine (SVM) classifier for a data matrix A whose input feature columns as well as individual data point rows are divided into groups belonging to different entities. Each ...
    • Probability of Unique Integer Solution to a System of Linear Equations 

      Recht, Benjamin; Mangasarian, Olvi (2009)
      We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique solution to the system that is integer: x ? {?1,1}n. We achieve this by reformulating ...
    • Proximal Knowledge-Based Classification 

      Fung, Glenn; Wild, Edward; Mangasarian, Olvi (2008-06-26)
      Prior knowledge over general nonlinear sets is incor- porated into proximal nonlinear kernel classification problems as linear equalities. The key tool in this incorporation is the conversion of general nonlinear prior ...
    • Radiosurgery Treatment Planning via Nonlinear Programming 

      Shepard, David; Lim, Jinho; Ferris, Michael (2001-01)
      The Gamma Knife is a highly specialized treatment unit that pro- vides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment ...
    • Robust Linear and Support Vector Regression 

      Musicant, David; Mangasarian, Olvi (2000-09)
      The robust Huber M-estimator, a differentiable cost function that is quadratic for small errors and linear otherwise, is modeled exactly, in the original primal space of the problem, by an easily solvable simple convex ...
    • RSVM: Reduced Support Vector Machines 

      Mangasarian, Olvi; Lee, Yuh-Jye (2001-01)
      An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset ...
    • Semismooth Support Vector Machines 

      Munson, Todd; Ferris, Michael (2000-11-29)
      The linear support vector machine can be posed as a quadratic pro- gram in a variety of ways. In this paper, we look at a formulation using the two-norm for the misclassi cation error that leads to a positive de - nite ...