Discrimination Analysis for Predicting Defect-Prone Software Modules

Algorithm 1

Kernel discrimination classifier (KDC).

Require:

 Normalized training data, 𝑇_𝑟;

 Labels vector of the training data, 𝑌;

 Normalized test data, 𝑇_𝑒;

 Kernel type, kernel;

Ensure:

 KDC classifier, 𝑀;

(1)  𝐾=kernelize 𝑇_𝑟,𝑇_𝑟,𝑘𝑒𝑟𝑛𝑒𝑙,𝑘𝑒𝑟𝑛𝑒𝑙𝑝𝑎𝑟𝑎𝑚;

  𝐾_𝑡=kernelize 𝑇_𝑟,𝑇_𝑒,𝑘𝑒𝑟𝑛𝑒𝑙,𝑘𝑒𝑟𝑛𝑒𝑙𝑝𝑎𝑟𝑎𝑚;

(2)  ℓ=𝑠𝑖𝑧𝑒 (𝐾,1);

(3)  ℓ⁺=(∑𝑌+ℓ)/2;

(4) 𝑌⁺=0.5∗(𝑌+1);

(5)  𝑒𝑙𝑙⁻=ℓ−ℓ⁺;

(6)  𝑌⁻=𝑌⁺−𝑌;

(7)  𝑡=𝑠𝑖𝑧𝑒 𝐾_𝑡,2;

(8)  Υ=𝑜𝑛𝑒𝑠 (ℓ,1)+𝑌∗(ℓ⁻−ℓ⁺/ℓ⁻¹);

(9)  𝜏⁺=2∗ℓ⁻/(ℓ∗ℓ⁺);

(10) 𝜏⁻=2∗ℓ⁺/(ℓ∗ℓ⁻);

(11) 𝐵=diag(Υ)−𝜏⁺∗𝑌⁺∗𝑌⁺−(𝜏⁻∗𝑌⁻)∗𝑌⁻;

(12) 𝑇=𝐵∗𝐾+𝜆∗𝑒𝑦𝑒(ℓ,ℓ)𝑌⁻¹;

(13) 𝑇^′_𝑟=𝑇∗𝑇_𝑟, 𝑇^′_𝑒=𝑇∗𝑇_𝑒;

(14) Collecting the neighbourhoods of 𝑥^′∈𝑇_𝑒 using (12);

(15) Calculate the mean distances using (13);

(16) Classify 𝑥 as 𝑀(𝑥)=argmin𝐷^𝑖_NEC;

(17) return   𝑀;