Now showing items 21-40 of 46

    • 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 ...
    • 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, ...
    • Finite Newton Method for Lagrangian Support Vector Machine Classi cation 

      Mangasarian, Olvi; Fung, Glenn (2002)
      An implicit Lagrangian [19] formulation of a support vector machine classi er that led to a highly e ective iterative scheme [18] is solved here by a nite Newton method. The proposed method, which is extremely fast and ...
    • 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. ...
    • 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 ...
    • Support Vector Machine Classi cation via Parameterless Robust Linear Programming 

      Mangasarian, Olvi (2003)
      We show that the problem of minimizing the sum of arbitrary-norm real distances to misclassi ed points, from a pair of parallel bounding planes of a classi cation problem, divided by the margin (distance) be- tween the ...
    • Breast Tumor Susceptibility to Chemotherapy via Support Vector Machines 

      Mangasarian, Olvi; Fung, Glenn (2003)
      Support vector machines (SVMs), utilizing RNA signature measurements, were used to generate a classi er to distinguish breast cancer patients that are partial-responders to chemotherapy treatment, from patients that are ...
    • 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 ...
    • Feature Selection in k-Median Clustering 

      Wild, Edward; Mangasarian, Olvi (2004)
      An e ective method for selecting features in clustering unlabeled data is proposed based on changing the objective function of the standard k-median clustering algorithm. The change consists of perturbing the objective ...
    • 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 ...
    • Absolute Value Equations 

      Meyer, Robert; Mangasarian, Olvi (2005)
      We investigate existence and nonexistence of solutions for NP-hard equations in- volving absolute values of variables: Ax ? |x| = b, where A is an arbitrary n � n real matrix. By utilizing an equivalence relation to the ...
    • 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 ...
    • 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 ...
    • Chunking for Massive Nonlinear Kernel Classification 

      Thompson, Michael; Mangasarian, Olvi (2006)
      A chunking procedure [2] utilized in [18] for linear classifiers is proposed here for nonlinear kernel classification of massive datasets. A highly accurate algorithm based on nonlinear support vector machines that ...
    • 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 ...
    • Exactness Conditions for a Convex Differentiable Exterior Penalty for Linear Programming 

      Wild, Edward; Mangasarian, Olvi (2007)
      Sufficient conditions are given for a classical dual exterior penalty function of a linear program to be independent of its penalty parameter. This ensures that an exact solution to the primal linear program can be obtained ...
    • 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 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 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 ...
    • 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 ...