# Minimum numbers of support vectors

I'm trying to understand the concept of SVM. Consider linearly separable data $$\{(x_i , y_i )\}_{i=1}^n , x_i \in \mathbb R^d , y_i \in \{−1, 1\}. \text{Let}\ \ \{x | w^T x + b = 0\}$$ be the margin-maximizing hyperplane that separates the data. Intuitively I understand that since there is a classification problem with at least 2 classes, there should be at least two support vectors (one for each class). But is there any formal proof of that (the minimum number of support vectors is 2)? And could there be more than two support vectors? If so, can you give an example?

• I think it's three. Two from one side of the plane and only one from the other side (for 2-dimensional input space). As both the two margins are parallel to each other, only one point is sufficient to designate the other line. Oct 6 '20 at 9:56

There is an answer on this question: https://stats.stackexchange.com/questions/259290/theoretical-minimum-number-of-support-vectors

Also, follow the links there to see more...

Consider a "machine" being the dividing line and the "support vectors" being the observations with their attributes. It is generally a binomial classification problem. For that you need at least two observations.