On Software Defect Prediction Using Machine Learning

Algorithm 1

AKPLSC.

Input: Labeled and unlabeled data sets, 𝐿 and 𝑈; number of components, 𝑘.

Output: Asymmetric Kernel Partial Least Squares Classifier, 𝐻;

Method:

(1) 𝐾_𝑖𝑗=𝜅𝑥_𝑖,𝑥_𝑗,𝑖,𝑗=1,…,ℓ,𝑥_𝑖,𝑥_𝑗∈𝐿;

(2) 𝐾₁=𝐾,𝑌=𝑌, where 𝐾 is the kernel matrix, 𝑌 is the label vector.

(3) for  𝑗=1,…,𝑘   do

(4)  𝛽_𝑗=𝛽_𝑗/𝛽_𝑗, where 𝛽_𝑗 is a projection direction.

(5)  repeat

(6)    𝛽_𝑗=𝑌𝑌^′𝐾_𝑗𝛽_𝑗

(7)    𝛽_𝑗=𝛽_𝑗/𝛽_𝑗

(8)  untill convergence

(9)  𝜏_𝑗=𝐾_𝑗𝛽_𝑗, where 𝜏_𝑗 is the score

(10)  𝑐_𝑗=𝑌^′𝜏_𝑗/𝜏_𝑗², where 𝑐_𝑗 is the direction of the score

(11)  𝑌=𝑌−𝜏_𝑗𝑐^′_𝑗, where 𝑌 is the deflation of 𝑌

(12)  𝐾_𝑗+1=(𝐼−𝜏_𝑗𝜏^′_𝑗/𝜏_𝑗²)𝐾_𝑗(𝐼−𝜏_𝑗𝜏^′_𝑗/𝜏_𝑗²)

(13) end for

(14) 𝐵=[𝛽₁,…,𝛽_𝑘],𝑇=[𝜏₁,…,𝜏_𝑘]

(15) 𝛼=𝐵(𝑇^′𝐾𝐵)⁻¹𝑇^′𝑌, where 𝛼 is the vector of dual regression coefficients

(16) Calculate 𝑏̂ according to (4);

(17) 𝐻(𝑥)=sign∑^ℓ_𝑖=1𝛼_𝑖𝜅𝑥_𝑖,𝑥−𝑏̂,𝑥∈𝑈;

(18) return   𝐻;

End Algorithm AKPLSC.