A Robust Hybrid Approach Based on Estimation of Distribution Algorithm and Support Vector Machine for Hunting Candidate Disease Genes

Algorithm 1

The step-by-step recipe for the computational algorithm of the EDA-SVM approach.

Step  1. 𝑀₀←Read gene expression profile matrix from database, 𝑚 is the number of genes in 𝑀₀.

Step  2. 𝐷₀←Generate 𝑁 individuals (the initial population) randomly. Each individual has an 𝑚-

length vector of bits of either 1 or 0.

Step  3. For each individual 𝑗 in 𝐷₀, determine:

 𝐺_𝑗←a gene subset corresponding to individual 𝑗. If bit i equals to 1, include 𝑔_𝑖 in the subset.

 𝑀_𝑗←gene expression profile submatrix.

 Fitness_𝑗←eval(𝑀_𝑗).

Step  4. 𝐷^𝑟_𝑙←retain 𝑁/2 individuals with the highest evaluations.

Step  5. 𝑀 arg inal(𝑧_𝑖,𝑙)←calculate marginal distribution of variable 𝑧_𝑖 of bit i based on 𝐷^𝑟_𝑙 by

using the formula: 𝑀arginal(𝑧_𝑖,𝑙)=∑^𝑁/2_𝑗=1𝑧^𝑗_𝑖/(𝑁/2), where 𝑧^𝑗_𝑖 is the value of the variable 𝑧_𝑖 in

individual 𝑗.

𝑀_weight(𝑧_𝑖,𝑙)← calculate weight of 𝑧_𝑖 corresponding to feature 𝑖 based on 𝐷^𝑟_𝑙.

𝑀_weight(𝑧_𝑖,𝑙)=∑^𝑁/2_𝑗=1Pre_weight(𝑧^𝑗_𝑖)/(𝑁/2), where Pre_weight(𝑧^𝑗_𝑖) is weight of bit 𝑖 in

individual 𝑗.

Pr𝑜𝑏(𝑧_𝑖,𝑙+1)←compute probability distribution 𝑧_𝑖 of each bit 𝑖, which is written

mathematically as:

Pr𝑜𝑏(𝑧_𝑖,𝑙+1)=𝑙𝑟𝛽_𝑖∗Pr𝑜𝑏(𝑧_𝑖,𝑙)+(1−𝑙𝑟)∗(1−𝛽_𝑖)∗𝑀arginal(𝑧_𝑖,𝑙)∗𝑀_weight(𝑧_𝑖,𝑙).

𝑙𝑟∈(0,1) is learning rate. 𝛽_𝑖∈(0,1) is generated at random.

Step  6. 𝐷^new_𝑙+1←generate new 𝑁/2 individuals by sampling the probability distribution.

Step  7. 𝐷_𝑙+1←𝐷^𝑟_𝑙∪𝐷^new_𝑙+1.

Step  8. 𝐷₀←𝐷_𝑙+1.

Step  9. End←output the optimal individual based on the evaluation with: fitness_𝑗=eval(𝑀_𝑗).