Theoretical: Minimum Number of Support Vectors I wanted to check if I am understanding the concept of the support vectors correctly. Let's say I am not using any kind of kernel, and it is a hard-margin SVM.
In this case, whatever the number of the dimensions is for our features, the minimum possible number of support vectors equals to 2 (1 for +, 1 for -). Am I correct? Do we still need more support vectors even in such an ideal case in $R^{d}$?
 A: Yes. The minimum number of support vectors is two for your scenario. You don't need more than two here.

All of the support vectors lie exactly on the margin. Regardless of the number of dimensions or size of data set, the number of support vectors could be as little as 2.
Reference: https://stackoverflow.com/questions/9480605/what-is-the-relation-between-the-number-of-support-vectors-and-training-data-and


A: Unfortunately the figure provided in the answer by @SmallChess still has 3 support vectors. The answer is correct - the minimum number of support vectors is 2. The best way to understand this issue is the convex hull model of SVM (for instance http://www.robots.ox.ac.uk/~cvrg/bennett00duality.pdf). The minimum case will have two convex hulls where the minimum distance between them is the distance between two vertices of the hull
A: If the training data involves only one class (which is a trivial problem) then there is no support vector at all.
Reference: Learning From Data - A Short Course, by Yaser S. Abu-Mostafa, Malik Magdon-Ismail and Hsuan-Tien Lin. e-Chapter 8, Exercise 8.12 and Page 31. 
