رياضى مهندسى بيشرفته هوش مصنوعى

Assume distance of two instances 𝑥 and 𝑐 is defined as 𝐷 𝑑 (𝑥, 𝑐) = ‖𝑥 − 𝑐‖𝑑 as the 𝑑-degree norm of their difference vector. For a set of instances 𝑋 = {𝑥𝑖 }, a representor 𝑐 can be defined with a deviation vector 𝑽 𝒅 (𝒄) such that its i th element is equal to the distance of 𝑥𝑖 from c, i.e. 𝑉𝑖 𝑑 (𝑐) = 𝐷𝑑(𝑥𝑖 , 𝑐). Then 𝑒 𝑑,𝑑 ′ (𝑋, 𝑐) as deviation of X respect to c is the norm of 𝑉 𝑑 (𝑐) with degree 𝑑 ′ . Both d’ and d can be from any degrees of 0, 1, 2 or ∞. Then, given a set of instances 𝑋 (dataset of Iris can be downloaded from UCI repository), find the representator 𝑐 of 𝑋 to minimize deviation vector associated with each pair of degrees 𝑑 and 𝑑 ′ from the following set: