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Suppose we have a set of $n > 1$ data points in $\mathbb{R}^2$ labeled either positive or negative. This set is linearly separable. Suppose that I'm searching for a the largest margin hyperplane of this set by using a SVM classifier.

It is possible to find such a data set that would result in having only one support vector? If no, what is the proof that the number of support vector must be at least 2?

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I have never seen a proof for this but it is intuitive that you cannot have only one support vector. Consider all pairs of positive-negative data points. The pair that is closest to each other will always be in the set of the support vectors. So we have at least two points

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