Thanks, this really helps. I think I'm getting a better picture. You said:
"where as K is a matrix k(x,y) will be only an entry scalar in matrix K."
I think I understand, but based on what you said is my following interpretation correct?
#1 k(x,y) is a kernal function (which produces a scaler that becomes and entry in matrix K)
If that is true, then does k(x,y) produce a dot product only between xi and xj (elements of the matrix X) or are they dot products also between x and y?
I'm thinking the entries in the kernal matrix are only dot products of xi and xj given your pseudocode , and y is just a 'label'.
But, I've also seen 'kernal functions' depicted in 2 different ways:
gaussian kernal: k(x,y) = exp(-||x-y||^2 / sigma^2)
gaussian kernal: k(xi,xj) = exp(-||xi-xj||^2 / sigma^2)
So I'm still confused on the notation about what are the 'inputs' into the kernel function, are the elements only of some matrix X, or can they also contain elements of Y?
Thanks.
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