InterJournal Complex Systems, 3123
Status: Submitted
Manuscript Number: [3123]
Submission Date: 130701
Comment on “robustness and regularization of support vector machines” by H. Xu, etc., (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2
Author(s): Yahya Forghani ,Hadi Sadoghi Yazdi

Subject(s): CX.66

Category: Brief Article

Abstract:

This paper comments on the published work dealing with robustness and regularization of support vector machines (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2009) by H. Xu, etc. They proposed the following theorem: For any x∈R^n,w∈H and c>0, sup┬(‖δ‖≤c)⁡〈w,Φ(x-δ) 〉=sup┬(‖δ_ϕ ‖_H≤√(2f(0)-2f(c)))⁡〈w,Φ(x)-δ_ϕ 〉, where f(‖x-x\'‖ )=k(x,x\') is a kernel function, H is the RKHS space of k(.,.) and Φ(.) is the corresponding feature mapping. In this paper, we propose a counter example that rejects their theorem.

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