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Related Experiment Videos

Properties of support vector machines

M Pontil1, A Verri

  • 1INFM, Dipartimento di Fisica dell'Università di Genova, 16146 Genova, Italy.

Neural Computation
|June 6, 1998
PubMed
Summary
This summary is machine-generated.

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Support vector machines (SVMs) use margin vectors to define decision surfaces. This study reveals how these surfaces change with regularization parameters and shows fewer support vectors (SVs) are often sufficient in finite feature spaces.

Area of Science:

  • Machine Learning
  • Pattern Recognition
  • Computational Mathematics

Background:

  • Support vector machines (SVMs) are key for pattern recognition.
  • SVMs identify decision surfaces using support vectors (SVs).
  • The decision surface is derived from quadratic programming involving a regularization parameter.

Purpose of the Study:

  • To mathematically analyze support vectors and decision surfaces in SVMs.
  • To investigate the influence of the regularization parameter on decision surface properties.
  • To determine the minimum number of SVs required for decision surface determination in finite feature spaces.

Main Methods:

  • Mathematical analysis of support vector properties.
  • Decomposition of the decision surface into orthogonal components.

Related Experiment Videos

  • Investigation of decision surface behavior concerning the regularization parameter.

    • Main Results:

    • The decision surface is shown to be a sum of two orthogonal terms: one dependent on margin vectors, the other on the regularization parameter.
    • Predictive insights into decision surface variations for small parameter changes are provided.
    • In finite-dimensional feature spaces (dimension m), m + 1 support vectors are typically sufficient to fully define the decision surface.

    Conclusions:

    • The mathematical properties of support vectors offer a deeper understanding of SVM decision surfaces.
    • The findings facilitate predicting decision surface evolution with regularization parameter adjustments.
    • A significant reduction in the number of support vectors is achievable in finite feature spaces, enhancing computational efficiency.