Feature Selection in Decision Systems: A Mean-Variance Approach

Algorithm 1

Forward Greedy Search Algorithm of Feature Selection based on

Mean-Variable in Decision Systems (FGSA-MVM):

Input: (𝑈, 𝐶∪ 𝐷, 𝑉, 𝑓), 𝜀

Output: 𝑟𝑒𝑑

(1) ∅→𝑟𝑒𝑑

(2) while 𝐶−𝑟𝑒𝑑≠∅

(3)  for each 𝑎_𝑖∈𝐶−𝑟𝑒𝑑

(4)   compute Sig_𝜎(𝑎_𝑖, 𝐵, 𝐷) = 𝜎(𝐵∪𝑎_𝑖,𝐷)−𝜎(𝐵,𝐷)

(5)  end for

(6)  select the attribute 𝑎_𝑘 such that

(7)   Sig_𝜎(𝑎_𝑘, 𝑟𝑒𝑑, 𝐷) = min_𝑖Sig_𝜎(𝑎_𝑖, 𝑟𝑒𝑑, 𝐷)

(8)  if Sig_𝜎𝑎_𝑘,𝑟𝑒𝑑,𝐷 < 𝜀

(9)    𝑟𝑒𝑑∪ 𝑎_𝑘→𝑟𝑒𝑑

(10) else

(11)   break

(12) end if

(13) end while

(14) return 𝑟𝑒𝑑