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Software defect prediction model based on distance metric learning

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Abstract

Software defect prediction (SDP) is a very important way for analyzing software quality and reducing development costs. The data during software lifecycle can be used to predict software defect. Currently, many SDP models have been proposed; however, their performance was not always ideal. In many existing prediction models based on machine learning, the distance metric between samples has significant impact on the performance of the SDP model. In addition, most samples are usually class imbalanced. To solve these issues, in this paper, a novel distance metric learning based on cost-sensitive learning (CSL) is proposed for reducing the impact of class imbalance of samples, which is then applied to the large margin distribution machine (LDM) to substitute the traditional kernel function. Further, the improvement and optimization of LDM based on CSL are also studied, and the improved LDM is used as the SDP model, called as CS-ILDM. Subsequently, the proposed CS-ILDM is applied to five publicly available data sets from the NASA Metrics Data Program repository and its performance is compared to other existing SDP models. The experimental results confirm that the proposed CS-ILDM not only has good prediction performance, but also can reduce the misprediction cost and avoid the impact of class imbalance of samples.

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Abbreviations

Tr:

Training sample set

S :

Sample set

Γ :

Label vector

Δ:

DML distance between two samples

\(s_{i}\) :

ith training sample

\(c_{i}\) :

ith class label

X T :

X’s transpose

\(X^{ - 1}\) :

X’s inverse

R d :

d-dimensional Euclidean space

t :

Number of training samples

m :

Number of class labels

Q :

A real-valued matrix

M :

A \(d \times d\) positive semi-definite matrix

Y :

A \(m \times m\) binary matrix

η :

A constant

\(n_{i}\) :

Number of samples with label \(c_{i}\)

\(l(i)\) :

Importance of \(c_{i}\)

\(\overline{m}\) :

Margin mean

\(\hat{m}\) :

Margin variance

\(\eta_{1} \,,\,\eta_{2}\) :

Trade-off parameters

\(\eta_{3}\) :

Penalty parameter

\(\varepsilon_{i}\) :

Misprediction cost of ith training sample

\(n_{\max }\) :

Number of samples in the majority class

\(n_{\min }\) :

Number of samples in the minority class

\(\kappa\) :

A nonnegative parameter

\(\tilde{\overline{m}}\) :

Cost-sensitive margin mean

\(\tilde{\hat{m}}\) :

Cost-sensitive margin variance

λ :

Coefficient vector

μ, ν :

Lagrangian multiplier vectors

S ( i ) :

ith standardized attribute vector

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  1. School of Computer, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Cong Jin

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Jin, C. Software defect prediction model based on distance metric learning. Soft Comput 25, 447–461 (2021). https://doi.org/10.1007/s00500-020-05159-1

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