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I know what Support Vector Machines (SVMs) are and how they work, but I regularly get confused by what exactly the support vectors are. In case of linearly separable data, the support vectors are ...
#1: Initial revision
by
mr Tsjolder
·
2023-08-01T20:32:41Z (over 1 year ago)
What are the support vectors in a soft-margin SVM
I know what Support Vector Machines (SVMs) are and how they work, but I regularly get confused by what exactly the support vectors are. In case of linearly separable data, the support vectors are those data points that lie (exactly) on the borders of the margins. After all, these are the only points that are necessary to compute the margin (through the bias term b) and therefore _support_ the solution. For soft-margin $C$-SVMs, however, I find the concept of support vectors less obvious. Of course, the data points on the border of the margin are still support vectors, but I always get confused about whether the points that are in the margin are support vectors or not. After all, only the points on the borders are used to compute the bias term $b$ (in the same way as for linearly separable data). Therefore, it could be argued that the margin is only supported by these points. However, there are [multiple](https://stats.stackexchange.com/questions/96497/effect-of-high-number-of-support-vectors) [sources](https://stats.stackexchange.com/questions/270187/svm-why-does-the-number-of-support-vectors-decrease-when-c-is-increased) that mention 1000+ support vectors, which would be impossible if only those on the border count. My question is thus: What exactly are the support vectors for a soft-margin SVM?