FAQ: Support Vector Machines - Support Vectors and Margins

This community-built FAQ covers the “Support Vectors and Margins” exercise from the lesson “Support Vector Machines”.

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I am unclear about the justification of the following sentence:

’ If you are using n features, there are at least n+1 support vectors.’

Any help is appreciated :slight_smile:


I have the same question here :face_with_raised_eyebrow:

It’s just a guess, but I think at least n+1 support vectors are required to identify the hyperplane uniquely. Let features be represented as variables x_1, ..., x_n. A hyperplane is represented by an equation like:

c_1 * x_1 + ... + c_n * x_n + b = 0

The method described in this lesson will be a quadratic programming problem which find the coefficients c_1, ..., c_n and the intercept b (n+1 unknowns) that maximize a certain distance under the constraints given by many linear inequalities. If we take out only the necessary ones out of those linear inequalities, I think that they would correspond to the support vectors, and the number of them would be at least n+1.

I think this is similar to the fact that at least n+1 equations are needed to uniquely identify the solution of equations with n+1 unknowns.