Supplementary material for : Generalizing from Several Related Classification Tasks to a New Unlabeled Sample
نویسندگان
چکیده
The function k : Ω×Ω→ R is called a kernel on Ω if the matrix (k(xi, xj))1≤i,j≤n is positive semidefinite for all positive integers n and all x1, . . . , xn ∈ Ω. It is well-known that if k is a kernel on Ω, then there exists a Hilbert space H̃ and Φ̃ : Ω→ H̃ such that k(x, x′) = 〈Φ̃(x), Φ̃(x)〉H̃. While H̃ and Φ̃ are not uniquely determined by k, the Hilbert space of functionsHk = {〈v, Φ̃(·)〉H̃ : v ∈ H̃} is uniquely determined by k, and is called the reproducing kernel Hilbert space (RKHS) of k.
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