Quote:
Originally Posted by udaykamath
I understand the step by step process in bounding the growth function B(N,k) in terms of recursion using x1,x2...xN data points using structural arrangements. I however started thinking, in a numerical data where x1,x2...xN is real numbers we cannot use this alpha + 2* Beta trick and use the polynomial bound by combination? What is the bounds when data is not binary ? Is it still Polynomial in N, and how?

You are correct. For nonbinary functions, the argument is more elaborate. This is addressed in Vapnik's book "Statistical Learning Theory" in much detail, and also appears in other books and papers.