(HARD VERSUS SOFT SVM)
Support Vectors: The set of sample points i ∈ I ∈ [m] corresponding to a hyperplane wT = 0 are called support vectors if wT (Tiyi ) = 1 Ci, where G > 0 is the slack variable in the case of Soft-SVM.
Hard-SVM is trained only on samples which are separable by the class of homogeneous half spaces. Prove or refute that the returned weight vector is a linear combination of the support vectors.
If we remove some samples from non-support vectors and train the hard-SVM again on the remaining samples, will we get a different weight vector? Prove your assertion.
A soft-SVM is trained on samples which are separable by the class of homogeneous halfspaces. If we remove some samples from non-support vectors and train the soft-SVM again on the remaining samples, are we guaranteed to get the same weight vector? Prove or refute the following claim: There exists > 0 such that for every sample D of m > 1 examples which is separable by the class of homogeneous halfspaces, the hard-SVM and the soft-SVM (with parameter A, i.e., the optimization problem is minimization of Allwl? + Ci1 G) learning rules return exactly the same weight vector.