Cost-Sensitive Feature Selection of Numeric Data with Measurement Errors

Algorithm 1

A backtracking algorithm to the FSMC problem.

Input:  (𝑈,𝐶,𝑑,{𝑉_𝑎},{𝐼_𝑎},𝑛,tc,mc), select tests 𝑅, current level test index lower bound 𝑙

Output:  A set of features 𝑅 with ATC and cmc, they are global variables

Method:  backtracking

(1)   for (𝑖=𝑙; 𝑖<|𝐶|; 𝑖 + +)  do

(2)   𝐵=𝑅∪{𝑎_𝑖}

    //Pruning for too expensive test cost

(3)  if  (tc(𝐵)>cmc)  then

(4)   continue;

(5)  end if

   //Pruning for non-decreasing total cost and decreasing misclassification cost

(6)  if  ((ATC(𝑈,𝐵)≥ATC(𝑈,𝑅)) and (mc(𝐵)<mc(𝑅)) then

(7)   continue;

(8)  end if

(9)  if  (ATC(𝑈,𝐵)<cmc)) then

(10)   cmc=ATC(𝑈,𝐵); //Update the minimal total cost

(11)   𝑅=𝐵; //Update the set of features with minimal total cost

(12)  end if

(13)  backtracking (𝐵,𝑖+1);

(14)  end for