support vector machines

Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

  • Martin Schmidt
  • Jan Pablo Burgard
  • Maria Eduarda Pinheiro
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

    Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

    Ensemble Methods for Robust Support Vector Machines using Integer Programming

  • Jannis Kurtz
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to develop models which are robust against small perturbations in the training data. We … Read more

    A sparse semismooth Newton based augmented Lagrangian method for large-scale support vector machines

  • Dunbiao Niu
  • Enbin Song
  • Peipei Tang
  • Qingsong Wang
  • Chengjing Wang
    • Categories Convex and Nonsmooth Optimization, Data-Mining Tags , ,

    Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However, the numerical difficulties of the SVMs will become severe with the increase of the sample size. Although there exist many … Read more

    Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition

  • Hamed Karimi
  • Mark Schmidt
  • Julie Nutini
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , ,

    In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Lojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older Polyak-Lojasiewicz (PL) … Read more

    A Feasible Direction Algorithm for Nonlinear Second-Order Cone Optimization Problems

  • Alfredo Canelas
  • Miguel Carrasco
  • Julio López
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications Tags , , ,

    In this work we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These problems consist of minimizing a nonlinear di erentiable objective function subject to some nonlinear second-order cone constraints. Given a point interior to the feasible set de nfined by the nonlinear constraints, the proposed approach computes a feasible and descent … Read more

    Clustering Categories in Support Vector Machines

  • Emilio Carrizosa
  • Dolores Romero Morales
  • Amaya Nogales-Gómez
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    Support Vector Machines (SVM) is the state-of-the-art in Supervised Classification. In this paper the Cluster Support Vector Machines (CLSVM) methodology is proposed with the aim to reduce the complexity of the SVM classifier in the presence of categorical features. The CLSVM methodology lets categories cluster around their peers and builds an SVM classifier using the … Read more

    Strongly Agree or Strongly Disagree?: Rating Features in Support Vector Machines

  • Emilio Carrizosa
  • Dolores Romero Morales
  • Amaya Nogales-Gómez
    • Categories (Mixed) Integer Linear Programming, Data-Mining Tags , , , ,

    In linear classifiers, such as the Support Vector Machine (SVM), a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features. Inspired by discrete psychometric scales, which measure the extent to which a factor is in agreement with a … Read more

    Incremental Accelerated Gradient Methods for SVM Classification: Study of the Constrained Approach

  • Nicolas Couellan
  • Sophie Jan
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , , , , , ,

    We investigate constrained first order techniques for training Support Vector Machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple calculations of Lagrange multipliers. Both primal and dual formulations are studied and compared. Experiments show that the … Read more

    Variable Neighborhood Search for parameter tuning in Support Vector Machines

  • Emilio Carrizosa
  • Belén Martín-Barragán
  • Dolores Romero Morales
    • Categories Data-Mining, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    As in most Data Mining procedures, how to tune the parameters of a Support Vector Machine (SVM) is a critical, though not sufficiently explored, issue. The default approach is a grid search in the parameter space, which becomes prohibitively time-consuming even when just a few parameters are to be tuned. For this reason, for models … Read more