No description support-vector-machines

Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs

  • Huiwen Jia
  • Siqian Shen
    • Categories Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification … Read more

    Feature selection in SVM via polyhedral k-norm

  • Manlio Gaudioso
  • Enrico Gorgone
  • Jean-Baptiste Hiriart-Urruty
    • Categories Data-Mining, Global Optimization Tags , , , ,

    We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo–norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate … Read more

    A Distributionally-robust Approach for Finding Support Vector Machines

  • Changhyeok Lee
  • Sanjay Mehrotra
    • Categories Data-Mining, Robust Optimization, Stochastic Programming Tags , , , ,

    The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population … Read more

    The Cyclic Block Conditional Gradient Method for Convex Optimization Problems

  • Amir Beck
  • Shoham Sabach
  • Edouard Pauwels
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , , ,

    In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when the blocks are chosen in a cyclic order. A global sublinear rate of convergence is established … Read more

    HIPAD – A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

  • Ioannis G. Akrotirianakis
  • Zhiwei (Tony) Qin
  • Amit Chakraborty
  • Xiaocheng Tang
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Quadratic Programming Tags , , , ,

    We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method … Read more

    An Improved Algorithm for the Solution of the Entire Regulation Path of Support Vector Machine

  • Chong-Jin Ong
  • Shiyun Shao
  • Jianbo Yang
    • Categories Data-Mining Tags , ,

    This paper describes an improved algorithm for the numerical solution to the Support Vector Machine (SVM) classification problem for all values of the regularization parameter, C. The algorithm is motivated by the work of Hastie \emph{et. al.} and follows the main idea of tracking the optimality conditions of the SVM solution for descending value of … Read more

    Adaptive Constraint Reduction for Training Support Vector Machines

  • Jin Hyuk Jung
  • Dianne P. O'Leary
  • AndrĂ© L. Tits
    • Categories Data-Mining, Quadratic Programming Tags , , ,

    A support vector machine (SVM) determines whether a given observed pattern lies in a particular class. The decision is based on prior training of the SVM on a set of patterns with known classification, and training is achieved by solving a convex quadratic programming problem. Since there are typically a large number of training patterns, … Read more

    A Coordinate Gradient Descent Method for Linearly Constrained Smooth Optimization and Support Vector Machines Training

  • Paul Tseng
  • Sangwoon Yun
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , , , , , , , ,

    Support vector machines (SVMs) training may be posed as a large quadratic program (QP) with bound constraints and a single linear equality constraint. We propose a (block) coordinate gradient descent method for solving this problem and, more generally, linearly constrained smooth optimization. Our method is closely related to decomposition methods currently popular for SVM training. … Read more

    Support Vector Machine via Sequential Subspace Optimization

  • Guy Narkiss
  • Michael Zibulevsky
    • Categories Data-Mining, Unconstrained Optimization Tags , , , ,

    We present an optimization engine for large scale pattern recognition using Support Vector Machine (SVM). Our treatment is based on conversion of soft-margin SVM constrained optimization problem to an unconstrained form, and solving it using newly developed Sequential Subspace Optimization (SESOP) method. SESOP is a general tool for large-scale smooth unconstrained optimization. At each iteration … Read more

    Interior point methods for massive support vector machines

  • Michael C. Ferris
  • Todd S. Munson
    • Categories Data-Mining Tags , ,

    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-definite matrix. Several formulations of the support vector machine fit into this category. An interesting feature of these particular problems is the volume … Read more