Parameter investigation of support vector machine classifier with kernel functions

Abstract

Support vector machine (SVM) is one of the well-known learning algorithms for classification and regression problems. SVM parameters such as kernel parameters and penalty parameter have a great influence on the complexity and performance of predicting models. Hence, the model selection in SVM involves the penalty parameter and kernel parameters. However, these parameters are usually selected and used as a black box, without understanding the internal details. In this paper, the behavior of the SVM classifier is analyzed when these parameters take different values. This analysis consists of illustrative examples, visualization, and mathematical and geometrical interpretations with the aim of providing the basics of kernel functions with SVM and to show how it works to serve as a comprehensive source for researchers who are interested in this field. This paper starts by highlighting the definition and underlying principles of SVM in details. Moreover, different kernel functions are introduced and the impact of each parameter in these kernel functions is explained from different perspectives.

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Notes

  1. 1.

    Some books and articles use the parameter \(\gamma =\frac{1}{2\sigma ^2}\).

  2. 2.

    The minimum distance was zero as mentioned before; but, with \(C=0\), the penalty parameter is completely neglected. Therefore, we consider that the minimum distance is 0.1.

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Correspondence to Alaa Tharwat.

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Tharwat, A. Parameter investigation of support vector machine classifier with kernel functions. Knowl Inf Syst 61, 1269–1302 (2019). https://doi.org/10.1007/s10115-019-01335-4

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Keywords

  • Support vector machine (SVM)
  • Kernel functions
  • Radial basis function
  • Polynomial kernel
  • Gaussian kernel
  • Parameter optimization
  • Linear kernel