It is easy to compute the change in the dimension- ality of the feature space, when...

Transcribed Image Text:

It is easy to compute the change in the dimension- ality of the feature space, when a kernel is defined by a polynomial of the type (p+1)2 where p is the dot product in the original feature space. That is, K(x, z) = (x-z + 1)². Consider the more general case: given vectors x, z = R", and the constant d, define K(x, z) = (xz+1)d. This kernel corresponds to an implicit mapping o: R" → Rm, where m>>n (that is, m is much greater than n). Find an equation/expression relating m, n and d. Hint: Consider successively different values of n, for example n = 2,3,4 and d, for example d = 2, 3. It is easy to compute the change in the dimension- ality of the feature space, when a kernel is defined by a polynomial of the type (p+1)2 where p is the dot product in the original feature space. That is, K(x, z) = (x-z + 1)². Consider the more general case: given vectors x, z = R", and the constant d, define K(x, z) = (xz+1)d. This kernel corresponds to an implicit mapping o: R" → Rm, where m>>n (that is, m is much greater than n). Find an equation/expression relating m, n and d. Hint: Consider successively different values of n, for example n = 2,3,4 and d, for example d = 2, 3.

Answer rating: 100% (QA)

To find an equation lexpression relating m nand d w... View the full answer