Now showing items 14-33 of 46

    • Incremental Support Vector Machine Classi cation 

      Mangasarian, Olvi; Fung, Glenn (2001)
      Using a recently introduced proximal support vector ma- chine classi er [4], a very fast and simple incremental support vector machine (SVM) classi er is proposed which is capable of modifying an existing linear classi ...
    • Interior Point Methods for Massive Support Vector Machines 

      Munson, Todd; Ferris, Michael (2000-05-25)
      We investigate the use of interior point methods for solving quadratic programming problems with a small number of linear constraints where the quadratic term consists of a low-rank update to a positive semi-de nite matrix. ...
    • Knowledge-Based Linear Programming 

      Mangasarian, Olvi (2003)
      We introduce a class of linear programs with constraints in the form of implications. Such linear programs arise in support vector machine classi cation, where in addition to explicit datasets to be classi ed, prior knowledge ...
    • Knowledge-Based Nonlinear Kernel Classi ers 

      Shavlik, Jude; Mangasarian, Olvi; Fung, Glenn (2003)
      Prior knowledge in the form of multiple polyhedral sets, each belonging to one of two categories, is introduced into a reformulation of a nonlinear kernel support vector machine (SVM) classi er. The resulting formulation ...
    • Knowledge-Based Support Vector Machine Classi ers 

      Shavlik, Jude; Mangasarian, Olvi; Fung, Glenn (2001)
      Prior knowledge in the form of multiple polyhedral sets, each belonging to one of two categories, is introduced into a reformulation of a linear support vector machine classi er. The resulting formulation leads to a ...
    • Lagrangian Support Vector Machines 

      Musicant, David; Mangasarian, Olvi (2000)
      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 di erentiable convex ...
    • Large Scale Kernel Regression via Linear Programming 

      Musicant, David; Mangasarian, Olvi (1999)
      The problem of tolerant data tting by a nonlinear surface, in- duced by a kernel-based support vector machine [24], is formulated as a linear program with fewer number of variables than that of other linear programming ...
    • 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 ...