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Bounds on error expectation for support vector machines.

V Vapnik1, O Chapelle

  • 1AT&T Labs-Research, Ecole Normale Supérieure de Lyon, Lyon, France.

Neural Computation
|September 8, 2000
PubMed
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We introduce the span of support vectors (SV), a new geometrical concept that improves support vector machine (SVM) generalization. This span offers more accurate test error predictions for optimal model selection.

Area of Science:

  • Machine Learning
  • Computational Statistics
  • Pattern Recognition

Background:

  • Support Vector Machines (SVMs) are powerful classification algorithms.
  • Generalization ability is crucial for SVM performance.
  • Previous generalization bounds relied on the diameter of spheres containing support vectors.

Purpose of the Study:

  • Introduce a novel geometrical concept: the span of support vectors (SV).
  • Demonstrate the dependence of SVM generalization ability on this new concept.
  • Provide a more accurate measure for predicting test error and guiding model selection.

Main Methods:

  • Theoretical analysis to define and prove properties of the span of support vectors.
  • Experimental validation of the span's predictive accuracy for test error.

Related Experiment Videos

  • Comparison of the span with existing geometrical measures for SVM generalization.

    • Main Results:

    • The span of support vectors is a novel geometrical concept influencing SVM generalization.
    • The span's value is consistently smaller than the diameter of the minimal enclosing sphere.
    • Span-based test error prediction shows high accuracy, outperforming previous methods.

    Conclusions:

    • The span of support vectors offers a tighter and more informative measure of SVM generalization.
    • This new concept has direct applications in optimizing SVM model selection.
    • The span provides a more refined geometrical understanding of SVM behavior.