Now showing items 1-20 of 46

    • 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 ...
    • 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 ...
    • 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 ...
    • 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 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 ...
    • 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 ...
    • 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. ...
    • 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 ...
    • 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, ...
    • A Finite Newton Method for Classi cation Problems 

      Mangasarian, Olvi (2001)
      A fundamental classi cation problem of data mining and machine learning is that of minimizing a strongly convex, piecewise quadratic function on the n-dimensional real space Rn. We show nite termination of a Newton ...
    • Set Containment Characterization 

      Mangasarian, Olvi (2001)
      Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classi ers [7], is extended to the following: (i) Containment of one ...
    • 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 ...
    • 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 ...
    • Cross-Validation, Support Vector Machines and Slice Models 

      Voelker, Meta; Ferris, Michael (2001)
      We show how to implement the cross-validation technique used in ma- chine learning as a slice model. We describe the formulation in terms of support vector machines and extend the GAMS/DEA interface to allow for e cient ...
    • Data Mining via Support Vector Machines 

      Mangasarian, Olvi (2001)
      Support vector machines (SVMs) have played a key role in broad classes of problems arising in various elds. Much more recently, SVMs have become the tool of choice for problems arising in data classi - cation and mining. ...
    • SIMULATION OPTIMIZATION BASED ON A HETEROGENEOUS COMPUTING ENVIRONMENT 

      Ferris, Michael; Sinapiromsaran, Krung (2001)
      We solve a simulation optimization using a deterministic nonlinear solver based on the sample-path concept. The method used a quadratic model built from a collection of surrounding simulation points. The scheme does not ...
    • Survival-Time Classi cation of Breast Cancer Patients 

      Wolberg, William; Mangasarian, Olvi; Lee, Yuh-Jye (2001)
      The identi cation of breast cancer patients for whom chemother- apy could prolong survival time is treated here as a data mining prob- lem. This identi cation is achieved by clustering 253 breast cancer patients into ...
    • 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 ...
    • Slice Models in General Purpose Modeling Systems 

      Meta, Voelker; Ferris, Michael (2000-12-14)
      Slice models are collections of mathematical programs with the same structure but di erent data. Examples of slice models appear in Data Envelopment Analysis, where they are used to evaluate e ciency, and cross-validation, ...