Linear hyperplanes as classifiers. Usman Roshan. Hyperplane separators. Hyperplane separators. w. Hyperplane separators. w. Hyperplane separators. r. x p. x. w. Hyperplane separators. r. x p. x. w. Nearest mean as hyperplane separator. m 2. m 1.
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m1 + (m2-m1)/2
where y is -1 if the point is on the left side of
the plane and +1 otherwise.
Distance of point x (with label y) to the hyperplane is given by
We want this to be at least some value
By scaling w we can obtain infinite solutions. Therefore we require that
So we minimize ||w|| to maximize the distance which gives us the SVM optimization
SVM optimization criterion
We can solve this with Lagrange multipliers.
That tells us that
The xi for which i is non-zero are called support vectors.
In practice we allow for error terms in case there is no