To convert non-convex to convex we are normalizing our data so that all point(of one class) will be on one side with distance greater than or equal to 1.Is there any guarantee that that there will always some points(which we call suppport vectors) at a distance of 1 after normalisation(assuming no outlier)
SVM convex with constraint
Yes surely there will be support vectors which are at unit distance from the hyperplane equation. This is becaues in equation of hyperplane i.e. ax1 + bx2 + c = 0, there are three variables namely a,b,c and distance of the point from the line will be (ax1 + bx2 + c)/sqrt(a^2 + b^2). and always when you apply the algorithm these variables will arrange themself that the hyperplane is exactly in between the two different clusters of classes.
Keep it mind that no outliers will be there in this case, that means you will be able to separate clusters of classes without any error. That is why we don’t stop here and proceed further for Pegasos algorithm, to deal with outliers as well.
This is helpful …thanks
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