(still under construction: sorry for the inconvenience...)

We have seen that the SVM and Gabriel graph classifiers have produced similar boundaries in two complex nonlinear cases. [Expand.]

However, it is not always the case that similar boundaries are computed. Take the following set of points:

[image of datapoints]

This results in the following boundaries:

[image of boundaries]

[Under construction: counterexamples of some observations in paper, SVM as subset of Gabriel graph]

Gabriel-editing Before SVM Training

One drawback to SVMs is the training time required to compute the appropriate boundary. It has been suggested that it may be of interest to use Gabriel-editing to simplify the training set before computing the SVM boundary.

Although this may work in some cases, Gabriel-editing will potentially lead to misclassification of training points from the original dataset. Take for example the results computed for the following dataset:

This results in the misclassification of a large group of points in the bottom left corner for the computed Gabriel-edited support vectors: