Neighborhood Rough Set Reduction-Based Gene Selection and Prioritization for Gene Expression Profile Analysis and Molecular Cancer Classification

Algorithm 1

A heuristic breadth-first search algorithm based on neighborhood rough set (HBFSNRS).

Input   ⟨𝑆,𝐺,𝐷⟩ , 𝛿, 𝜃, 𝑝, 𝜔, 𝑟_Max, and Depth//𝛿 is the threshold to control the size of the neighborhood, 𝜃 is the

threshold of increment, 𝑝 is the number of the preselected genes, 𝜔 is the search breadth, 𝑟_Max is a given maximal

dependency function value and Depth is the upper bound of searching depth.

Output  RED is the pool to contain the selected gene subsets red.

Step 1: For each 𝑔_𝑖∈𝐺//Compute p-value by KWRST

     𝑃_𝑖=KWRST(𝑔_𝑖);

       End

Step 2: 𝑔𝑔=sort(𝑃, ‘‘ascend’’); //Rank genes by 𝑃 in ascending order

Step 3: 𝐺^∗=Select(𝐺,𝑔𝑔,𝑝); //Select he 𝑝 top-ranked genes as the initial gene set 𝐺^∗ by 𝑃

Step 4: For each 𝑔_𝑖∈G^∗//Let RED={{𝑔₁},{𝑔₂},...{𝑔_𝑝}} be a set of gene subsets where each

     𝑔_𝑖→red_𝑖; //gene subset only has an informative gene.

     red_𝑖→RED;

   End

Step 5: 𝑖𝑡𝑒𝑟=1; //The times of iteration.

Step 6: For each red_𝑗∈RED

    For each 𝑔_𝑘∈𝐺^∗−red_𝑗

     red_𝑗∪𝑔_𝑘→RED; //Adding genes not listed in red_𝑗 to red_𝑗 and save it as elements of RED

     𝛾_{red𝑗∪𝑔𝑘}(𝐷)=Card(Pos_{red𝑗𝑘∪𝑔}(𝐷))/Card(𝑆); //Compute dependence degree of 𝐷 to red_𝑗∪𝑔_𝑘.

    End

       End

Step 7: 𝑟𝑟=sort(𝑟, ‘‘descending’’); //Rank gene subsets by𝑟in descending order

      RED=Select(RED,𝑟𝑟,𝑤); //Select 𝜔 top-ranked gene subsets to reconstruct RED.

Step 8: If (max_iter(𝛾)>=𝑟_Max) or abs(max_iter(𝑟)−max_iter−1(𝑟))<𝜃 or (iter=Depth)

     Break;  //here, we define max₀(𝑟)=0

     Else

    iter=iter+1;

    Go to step 6;

       End