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Machine Learning by Sergios Theodoridis

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Classification

In this case, a typical choice is to project on the half-space, Section 8.6.2, formed by the hyperplane

ynfn1,κ(,xn)=ρ,

si310_e

and the corresponding projection operator becomes

Pk(fn1)=fn1+βkκ(,xk),

si311_e

where

βk=ρykfn1,κ(,xk)κ(xk,xk),ifρykfn1,κ(,xk)>0,0,otherwise.

si312_e  (11.110)

Recall that the corresponding half-space is the 0-level set of the hinge loss function, ρ(yn,f(xn)) defined in (11.59).

Thus, for both cases, regression ...

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