Friday 4 February 2011

Musings on Semi-Supervised Graph Learning

Marginal Distribution P supported by low dimensional manifold M

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