# Minimum number of support vectors? [closed]

I'm learning SVM and its written everywhere that the minimal number of support vectors is 2? But I couldn't find any formal proofs of that. Why cant there be less than 2 support vectors? Can somebody give an intuitive way of understanding that and a formal explanation?

## closed as off-topic by Chris Godsil, მამუკა ჯიბლაძე, Gabriel C. Drummond-Cole, Mark Wildon, kodluDec 17 '18 at 3:58

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Gabriel C. Drummond-Cole, Mark Wildon, kodlu
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You have a training dataset of points $$x_1,\dots,x_n$$, say in $$V:=\mathbb R^d$$, each classified as green or blue (say). The dataset is linearly separable if there is a hyperplane $$H$$ in $$V$$ such that all the green data points are in one open half-space (say $$H^+$$) bounded by $$H$$ and all the blue data points are in the other open half-space (say $$H^-$$) bounded by $$H$$. Suppose that such a separating hyperplane $$H$$ indeed exists. (Otherwise, a standard remedy is to map (possibly nonlinearly) the dataset into another space, possibly of a higher dimension.) The separating hyperplane $$H$$ is called the maximum-margin hyperplane if the minimal distance $$d(H):=\min_i d(x_i,H)$$ from the dataset points $$x_i$$ to $$H$$ is maximal over all choices of separating hyperplanes; we are assuming here that the green and blue subsets of the dataset are each nonempty. See the picture in Section "Linear SVM". The points $$x_i$$ of the dataset that are the closest ones to the maximum-margin hyperplane $$H$$ are called the support vectors. Clearly, there is at least one such vector in each of the open half-spaces, $$H^\pm$$. (In the picture, the boundaries of the corresponding dots are highlighted as black.) So, there are at least two support vectors: at least one of them on either side of the maximum-margin hyperplane.