We know that in SVM, support vectors that determine the position and orientation of the hyperplane are close to the boundary (close to the plane).
In the simulation I did most of the support vectors are near the plane which makes sense but there are a few that are far from the plane. Is it reasonable for example because of optimization solver which is numerical?
Thank you
The answer to your question is yes! Related to your query, I suggest:
https://www.di.ens.fr/~mallat/papiers/svmtutorial.pdf
Yes we can have support vectors at a greater distance from plane. Basically the support vectors are those data points that decides the margins . The more distance of support vectors from decided margin means more appropriate classifications. You can take a look to below link.
https://nlp.stanford.edu/IR-book/html/htmledition/support-vector-machines-the-linearly-separable-case-1.html
Your situation with SVM can be described as follow:
In SVM the data points that are closest to the hyperplane are used to measure the margin; hence these data points are termed support vectors. Consequently, the number of support vectors is small. If the two classes are not linearly separable, the SVM tries to find the hyperplane that maximizes the margin while, at the same time, minimizing a quantity proportional to the number of misclassification errors.
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