Now showing items 1-20 of 35

    • Absolute Value Equation Solution via Dual Complementarity 

      Mangasarian, Olvi (2011)
      By utilizing a dual complementarity condition, we propose an iterative method for solving the NPhard absolute value equation (AVE): Ax?|x| = b, where A is an n�n square matrix. The algorithm makes no assumptions on the ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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. ...
    • Equivalence of Minimal L0 and Lp Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p 

      Mangasarian, Olvi; Fung, Glenn (2011)
      For a bounded system of linear equalities and inequalities we show that the NP-hard ?0 norm minimization problem min ||x||0 subject to Ax = a, Bx ? b and ||x||? ? 1, is completely equivalent to the concave minimization ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...