Ben Goodrich

Monash University (Australia), Melbourne, Victoria, Australia

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Publications (3)0 Total impact

  • Ben Goodrich · David Albrecht · Peter Tischer
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    ABSTRACT: We approach the problem of applying nearest point algorithms to train weighted SVMs by introducing the concept of Weighted Reduced Convex Hulls (WRCHs). We describe some of the theoretical properties of WRCHs and show how their vertices may be found. The introduction of WRCHs provides an essential tool for understanding how weighted SVMs work and why they are important. Further, they allow us to generalize the Schlesinger-Kozinec (S-K) nearest point algorithm to operate over WRCHs. The result is a nearest point algorithm which is capable of training weighted SVMs without the need for inflating the training set size.
    No preview · Article · Nov 2011
  • Ben Goodrich · David W. Albrecht · Peter E. Tischer
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    ABSTRACT: By considering the geometric properties of the Support Vector Machine (SVM) and Minimal Enclosing Ball (MEB) optimization problems, we show that upper and lower bounds on the radius-margin ratio of an SVM can be efficiently computed at any point during training. We use these bounds to accelerate radius-margin parameter selection by terminating training routines as early as possible, while still obtaining a guarantee that the parameters minimize the radius-margin ratio. Once an SVM has been partially trained on any set of parameters, we also show that these bounds can be used to evaluate and possibly reject neighboring parameter values with little or no additional training required. Empirical results show that, when selecting two parameter values, this process can reduce the number of training iterations required by a factor of 10 or more, while suffering no loss of precision in minimizing the radius-margin ratio.
    No preview · Conference Paper · Dec 2010
  • Ben Goodrich · David Albrecht · Peter Tischer
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    ABSTRACT: Geometric interpretations of Support Vector Machines (SVMs) have introduced the concept of a reduced convex hull. A reduced convex hull is the set of all convex combinations of a set of points where the weight any single point can be assigned is bounded from above by a constant. This paper decouples reduced convex hulls from their origins in SVMs and allows them to be constructed independently. Two algorithms for the computation of reduced convex hulls are presented – a simple recursive algorithm for points in the plane and an algorithm for points in an arbitrary dimensional space. Upper bounds on the number of vertices and facets in a reduced convex hull are used to analyze the worst-case complexity of the algorithms.
    No preview · Chapter · Nov 2009