Question: Consider a linear machine with discriminant functions gi(x) = wtix + w0i; i = 1,..., c and the decision rule: decide Wi if gi(x) >

Consider a linear machine with discriminant functions

gi(x) = wtix + w0i; i = 1,..., c

and the decision rule: decide Wi if gi(x) > gj(x) for all j not= i. Suppose that decision

regions Rk and Rl are contiguous.

(a) Find the equation of the hyperplane Hij that forms the boundary between them.

(b) Find the orthogonal projection of x onto the hyperplane Hij .

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