I am trying to understand the relationship between the weight vector, the support vectors, and the decision boundary. Suppose that I have, the direction of the decision hyperplane [0.5 0.5 0.5 0.5], positive support vector [1 2 3 4] and negative support vector [0 0 0 0]. How are they related mathematically?
Can I derive the weight vector based on this information?
Thank you, I am new to SVM.
if your SVM is without kernels, then the decision hyperplane IS the weight vector. You don't need the support vectors anymore
if using kernels, then the mapping is in a higher dimension and there's no simple relationship. See a similar question I asked some time ago, and in there you will also find a free book for SVMs that helped me a lot in understanding: reverse mapping of SVM kernel into original feature space