f* = argmin 1/n sum(E(x,y)) + norm
= sum a.K(x,y)
If P known introduce another regulizer term which is a penalty (Riemannian = Laplace operator) that reflects intrinsic structure.
f* = argmin 1/n sum(E(x,y)) + amb.norm + intr.norm
Most cases P is unknown we need estimates of P and norm from unlabeled examples
f* = argmin 1/n sum(E(x,y)) + amb.norm + intr.norm / (u +l)^2.f'Lf
Can be solved by a regularized least squares algorithm
If we disregard the labeled data it becomes:
f* amb.norm + f'Lf s.t. sum f(x) = 0 and f(x)^2 =1
Which gives the generalized eigen problem
P(amb.K + K.L.K)Pv = lam.P.K^2.P.v
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