CN103810101A - Software defect prediction method and system - Google Patents

Abstract

The invention provides a software defect prediction method and a software defect prediction system, which are used to solve the problem of low accuracy of the existing software defect prediction. Including: a dimensionality reduction processing unit, an SVM training unit, and a defect prediction unit; wherein step 1, performs dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, and obtains that each sample point in the first training data set is mapped to a low-dimensional The low-dimensional vector in the space obtains the second training data set that is made up of each low-dimensional vector; Step 2, supports vector machine SVM classifier is trained according to the second training data set, obtains the optimal classification of SVM classifier hyperplane function, and then obtain a trained SVM classifier; step 3, perform defect prediction on the software to be predicted according to the trained SVM classifier.

Description

A software defect prediction method and software defect prediction system

technical field

The invention relates to the field of software security, in particular to a software defect prediction method and a software defect prediction system. the

Background technique

Software defect prediction technology was born in the 1970s, and its main function is to guide quality assurance work and provide high-value reference for balancing software costs. Software defect prediction is mainly divided into dynamic prediction and static prediction. At present, main researches are concentrated on static prediction. The present invention belongs to distribution prediction technology in static prediction. Support Vector Machine (SVM for short) is a new machine learning method developed on the basis of statistical learning theory. It has many unique advantages in solving small sample, nonlinear and high-dimensional pattern recognition. The existing Software defect prediction mainly utilizes the support vector machine (SVM) tool to establish a prediction model to predict software defects. The patents related to software defect prediction mainly include: defect prediction method and system based on requirement change (publication number CN200910080742) and software defect priority prediction method based on improved support vector machine (publication number CN201210057888). the

The idea of the existing technology includes two parts, the dimensionality reduction of the data set and the optimization of the parameters of the support vector machine. For these two problems, the existing technology proposes different solutions and achieves certain results, but the existing technology The selected dimensionality reduction method has certain limitations. The result after dimensionality reduction cannot guarantee the integrity of the original data, nor is it the best embodiment of the intrinsic dimensionality. The software defect prediction technology itself is an operation on the data set, and the data The guarantee of completeness is of great significance to ensure the accuracy of prediction results. the

Contents of the invention

The invention provides a software defect prediction method and a software defect prediction system, which are used to solve the problem of low accuracy of the existing software defect prediction. the

A software defect prediction method, comprising the following steps:

Step 1. Perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, and obtain the low-dimensional vectors in which each sample point in the first training data set is mapped to the low-dimensional space, and obtain the first training data set composed of various low-dimensional vectors. Two training data sets;

Step 2, support vector machine SVM classifier is trained according to the second training data set, obtain the optimal classification hyperplane function of SVM classifier, and then obtain the trained SVM classifier;

Step 3, perform defect prediction on the software to be predicted according to the trained SVM classifier. the

The second training data set composed of various low-dimensional vectors obtained in step 1 adopts the following method:

1.1 Let the first training data set be {X ₁ ,X ₂ ,...,X _N },X _i ∈R ^D , where X _i is a vector belonging to D-dimensional space;

1.2 Calculating the K nearest neighbor points of each sample point _Xi in the first training data set;

1.3 Use the K neighbor points of each sample point to calculate the local reconstruction weight matrix W according to formula 1;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1

Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point _Xi using the j-th neighbor point; all sample points _Xi in the first training data set use the coefficients represented by their neighbor points to form the local reconstruction weight value matrix W;

1.4 Calculate the low-dimensional vector corresponding to each sample point according to the obtained local reconstruction weight matrix W and the neighbor points of the sample point according to formula 2;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2

Wherein, I is the identity matrix, M=(IW) ^T (IW).

Wherein step 2 described obtains the trained SVM classifier adopting the following method:

Solve the optimal classification hyperplane function of the SVM classifier according to formula 3

$\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3

Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, _ξi is the slack variable, and φ(x) is the kernel function used by the SVM classifier.

The above kernel function is a radial basis kernel function in the form of:

$K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4

where σ is the width parameter of the radial basis kernel function. the

In the above-mentioned optimal classification hyperplane function of the SVM classifier, the grid search method and the ten-fold cross-validation method are used to optimize the parameter C of the SVM classifier and the parameter σ of the kernel function, and find the one with the highest classification accuracy of the SVM. The value of the parameters C and σ to determine the optimal classification hyperplane function of the SVM classifier. the

The above-mentioned optimization of the parameter C of the SVM classifier and the parameter σ of the kernel function using the grid search method and the ten-fold cross-validation method includes: using the grid search method to value the parameters C and σ; obtaining the value range of C Search for all combinations of all values in σ and all values in the range of σ. the

The above-mentioned optimization of the parameter C and the kernel function parameter σ of the SVM classifier by using the grid search method and the ten-fold cross-validation method includes: obtaining the classification under this set of parameter values for each set of parameters C and σ selected Accuracy, using the ten-fold crossover method for verification, taking the group of parameters with the highest classification accuracy as the best parameter value; among them, using the ten-fold crossover method for verification refers to dividing the second data set into 10 subsets , 1 subset is used as the test set, and the remaining 9 subsets are used as the training set to obtain 1 classification accuracy rate under a selected set of parameters, and repeat this 10 times; to obtain 10 classification accuracy rates under this set of parameters, The average of the 10 classification accuracy rates is used as an index to evaluate the pros and cons of each group of parameters, and then, the average of the classification accuracy rates of each selected group of parameters is compared, and the group of parameters C, σ with the highest average number is used as the best parameter values. the

Among them, the software defect prediction according to the optimal classification hyperplane function adopts the following method:

First, use the LLE algorithm to reduce the dimensionality of the data set of the forecasting software;

Secondly, input the data set after dimension reduction into the trained SVM classifier and make a judgment; if the input data falls into the space without defects determined by the optimal classification hyperplane function, then Determine that the software module corresponding to the data does not contain a defect and mark it in the output result of the SVM classifier; if the input data falls into the defective space determined by the optimal classification hyperplane function, then determine that the The software modules corresponding to the above data contain defects and are marked in the output of the SVM classifier. the

A software defect prediction system, comprising: dimensionality reduction processing unit, SVM training unit and defect prediction unit;

The dimensionality reduction processing unit is used to perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, to obtain a low-dimensional vector in which each sample point in the first training data set is mapped to a low-dimensional space, and to obtain a low-dimensional vector composed of each low-dimensional The second training data set composed of vectors;

The SVM training unit is used to train the support vector machine SVM classifier according to the second training data set, obtain the optimal classification hyperplane function of the SVM classifier, and then obtain the trained SVM classifier;

The defect prediction unit is used to perform defect prediction on the software to be predicted according to the trained SVM classifier. the

Beneficial effects of the present invention:

In the software defect prediction method and software defect prediction system provided by the present invention, firstly, the local linear embedding algorithm is used to reduce the dimensionality of the training data set to ensure that the geometric structure of the sample points in the data set remains unchanged after dimensionality reduction, so that the dimensionality reduction data It can more completely reflect the various characteristics of the original data set. Secondly, according to the grid search algorithm, find the parameter C of the SVM and the parameter σ of the kernel function for optimization, and cooperate with the ten-fold cross-validation method to find the SVM with the highest classification accuracy. The value of that group of C and σ is determined as the optimal parameter, and the optimal classification hyperplane function of SVM is determined according to the optimal parameter, and the optimal classification hyperplane function is used for software defect prediction to improve the accuracy of software defect prediction. . the

Description of drawings

Fig. 1 is the block diagram of a kind of software defect prediction method that an embodiment of the present invention provides;

Fig. 2 is the flow chart of a kind of software defect prediction method that another embodiment of the present invention provides;

Fig. 3 is a block diagram of a software defect prediction system provided by another embodiment of the present invention. the

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the implementation manner of the present invention will be further described in detail below in conjunction with the accompanying drawings. the

The technical idea of the present invention is aimed at the limitations of the existing dimensionality reduction methods, that is, the result after dimensionality reduction cannot guarantee the integrity of the data, nor is it the best embodiment of the intrinsic dimensionality. The embodiment of the present invention adopts the locally linear embedding (LLE for short) algorithm to reduce the dimensionality of the software defect data set. The idea of the algorithm is to start from the spatial structure of the sample data and to ensure the geometric structure of the data sample after dimensionality reduction. Unchanged, so that the data after dimensionality reduction can more completely reflect the various characteristics of the original data set. The software defect prediction technology itself is an operation on the data set. A more complete reflection of the characteristics of the original data will improve the accuracy of the prediction results. is extremely important. the

An embodiment of the present invention provides a software defect prediction method. Fig. 1 is a block diagram of a software defect prediction method provided by an embodiment of the present invention, referring to Fig. 1, the method includes:

Step S100: Perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, obtain the low-dimensional vectors in which each sample point in the first training data set is mapped to the low-dimensional space, and obtain the first training data set composed of various low-dimensional vectors Two training data sets;

Step S110: Train the support vector machine SVM classifier according to the second training data set, obtain the optimal classification hyperplane function of the SVM classifier, and then obtain the trained SVM classifier;

Step S120: Perform defect prediction on the software to be predicted according to the optimal classification hyperplane function. the

In this embodiment, the first training data set is subjected to dimensionality reduction processing according to the local linear embedding algorithm LLE, and the low-dimensional vectors in which each sample point in the first training data set is mapped to a low-dimensional space are obtained. The second training data set composed includes:

Let the first training data set be {X ₁ , X ₂ ,...,X _N }, X _i ∈ R ^D where X _i is a vector belonging to D-dimensional space;

Calculate the K nearest neighbor points of each sample point _Xi in the first training data set;

Use the K nearest neighbor points of each sample point to calculate the local reconstruction weight matrix W according to formula 1;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1

Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point _Xi using the j-th neighbor point; all sample points _Xi in the first training data set use the coefficients represented by their neighbor points to form the local reconstruction weight value matrix W;

Calculate the corresponding low-dimensional vector of each sample point according to the obtained local reconstruction weight matrix W and its neighbor points according to formula 2;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2

Wherein, I is the identity matrix, M=(IW) ^T (IW).

In the present embodiment, support vector machine SVM classifier is trained according to the second training data set, and the optimal classification hyperplane function of obtaining SVM classifier includes:

Solve the optimal classification hyperplane function of the SVM classifier according to formula 3

$\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3

Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, _ξi is the slack variable, and φ(x) is the kernel function used by the SVM classifier.

In this embodiment, the kernel function is a radial basis kernel function in the form:

$K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4

where σ is the width parameter of the radial basis kernel function. the

Fig. 2 is a flow chart of a method for software defect prediction provided by another embodiment of the present invention; referring to Fig. 2, specifically, the embodiment of the present invention can be specifically divided into three parts, the first part is to reduce the training data set Dimension processing: this part includes steps S200 and S210: the second part includes step S220; the third part then includes step S230.

Step S200: Obtain the first training data set used in software defect prediction;

Step S210: Use the LLE algorithm to perform dimensionality reduction on the first training data set; the data set used in this embodiment is the NASA MDP software defect data set widely used in research in the field of software defect prediction, which can be downloaded from the Internet . The dataset contains 13 sub-datasets, and each sub-dataset records the measurement attributes and flag bits of each module in NASA's actual software project, where the flag bit represents whether the module has defects. After the first training data set is obtained, dimensionality reduction processing is performed on the data set. Specifically, the dimensionality reduction steps can be divided into:

1) Let the first training data set be {X ₁ ,X ₂ ,...,X _N },X _i ∈R ^D , where R represents space and D represents dimension.

2) Determine the distance between each sample point and other sample points, the calculation formula is d _ij =||X _i -X _j ||, after calculating the distance between each sample point and other sample points, select Among them, the K with the shortest distance are taken as the nearest neighbor points;

3) Calculate the local reconstruction weight matrix W from the neighbor points of the sample point _Xi , so as to minimize the reconstruction error of the sample point, that is, to solve the optimization problem:

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1

Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point using the j-th neighbor point, and w _ij is also a weight, representing the contribution of the j-th neighbor point to the i-th sample point. Specifically, the LLE algorithm is used to reduce the dimension of the data set: for each sample point in the data set, the K nearest neighbor points of the sample point are used to represent the sample point. In this way, when each sample point is represented by a neighbor point, there are K coefficients representing the sample point. When a single neighbor point represents the sample point, the coefficient is a specific value, and the K coefficient of each sample point is The coefficients form a coefficient vector; the coefficient vectors of all sample points in the data set form a weight matrix W.

4) Then fix the local reconstruction weight matrix W obtained in the previous step, and solve the low-dimensional vector Y _i corresponding to each sample point _Xi according to the objective function. The objective function is:

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2

Wherein, I is an identity matrix, M=(IW) ^T (IW), and finally the 2nd to d+1 eigenvectors of M are the output results. Here, d represents the dimensionality of the sample points after dimensionality reduction, and the final output is d low-dimensional vectors.

After the above four steps, the low-dimensional vectors that each sample point in the first training data set is mapped to the low-dimensional space are obtained, and then the SVM classifier is trained with the second training data set composed of these low-dimensional vectors. the

In the second part, use the reduced data set to train the SVM classifier:

Step S220: Input the dimensionally reduced data set into the SVM classifier, optimize the parameters by combining the grid search method and the ten-fold cross-validation method, and train the SVM classifier. the

Wherein, the support vector machine SVM classifier is trained according to the second training data set, and the optimal classification hyperplane function of the SVM classifier is obtained, which specifically includes the following process:

The SVM classifier is trained using the dimensionally reduced second training data set, and the training process is to solve the optimal classification hyperplane of the SVM. the

Specifically, the problem of training SVM can be converted into a problem of convex quadratic programming:

$\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3

Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, ξ _i is the slack variable, and φ(x) is the kernel function selected for use. The penalty factor C determines how much attention is paid to the loss caused by outliers. Obviously, when the sum of the slack variables of all outliers is constant, the larger the fixed C, the greater the loss to the objective function, which implies You are very unwilling to give up these outliers. The most extreme case is that you set C to be infinite, so that as long as there is a slight outlier, the value of the objective function will immediately become infinite, and the problem will immediately become unsolvable. This degenerates into a hard margin problem. The value of the slack variable _ξi actually marks how far the corresponding point is out of the group. The larger the value, the farther the point is. The role of the kernel function is to transform the linear inseparable into linearly separable by mapping the data in the low-dimensional space to the high-dimensional space.

Since the radial basis kernel function has a wide convergence range, the radial basis kernel function is used as the kernel function of the SVM classifier in this embodiment. The form of the kernel function is:

$K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4

Introduce Lagrangian multipliers, use the standard Lagrangian duality principle to simplify and solve the aforementioned quadratic programming problem, and obtain a sign discriminant function:

$f\left(x\right)=\mathrm{sign}(\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{\mathrm{the\; y}}_{i}K(x_i,x)+b)$ Formula 5

For the determination of the penalty coefficient C in SVM and the parameter σ in the radial basis kernel function, in this embodiment, the grid search method and the ten-fold cross-validation method are used to search for the parameter C of the SVM classifier and the parameter σ of the kernel function. Optimum, find the value of the pair of parameters C and σ that makes the SVM classification accuracy the highest, so as to determine the optimal classification hyperplane function of the SVM classifier. the

Specifically, in this embodiment, a grid search method is used to determine the optimal values of parameters C and σ; that is, let these two parameters be divided into grids in a predetermined range and traverse all grids to take values, where , the value interval of C is set to [2 ^-10 ,2 ⁷ ], the value interval of σ is set to [2 ^-10 ,2 ³ ], the step size of both parameters is 0.1, and all All combinations of the value of σ and all the values in the value range of σ are searched.

In this embodiment, for each selected group of parameters C and σ, the classification accuracy rate under the value of this group of parameters is obtained, and the ten-fold crossover method is used for verification, and the group of parameters C, σ with the highest classification accuracy is selected. As the best parameter value; among them, the implementation process of using the ten-fold crossover method for verification is: divide the second data set into 10 subsets, 1 subset is used as the test set, and the remaining 9 subsets are used as the training set, and the selected 1 classification accuracy rate under a given set of parameters, repeating this 10 times; get 10 classification accuracy rates under this set of parameters, and use the average of these 10 classification accuracy rates as the criterion for evaluating the pros and cons of each set of parameters Index, and then compare the average of the classification accuracy of each selected set of parameters, and use the set of parameters C, σ with the highest average as the best parameter value. the

After finding the optimal parameter C, the value of σ, determine the optimal classification hyperplane function of the SVM classifier, and then obtain the trained SVM classifier. the

The third part: Use the trained SVM classifier to predict the defects of the software to be tested. the

Step S230: use the trained SVM classifier to predict software defects;

Specifically, in this embodiment, firstly, the data set of the forecasting software is subjected to dimensionality reduction processing using the LLE algorithm; if the input data falls into the space without defects determined by the optimal classification hyperplane function, then it is determined that The software module of the software module does not contain defects and is marked in the output result of the SVM classifier; if the input data falls into the defective space determined by the optimal classification hyperplane function, it is determined that the software module corresponding to the data contains defects and is in the Labeled in the output of the SVM classifier. the

In this embodiment, when the output result of the SVM classifier is displayed, if the software module has a defect, it will be marked with the letter Y. If the software module has no defects, it is marked with the letter N. the

Therefore, the software defect prediction method provided by the embodiment of the present invention uses a local linear embedding algorithm to perform dimension reduction processing on the training data set, ensuring that the geometric structure of the sample points in the data set remains unchanged after dimension reduction, so that the data after dimension reduction can be more complete. accurately reflect the various characteristics of the original data set. the

Yet another embodiment of the present invention also provides a software defect prediction system. FIG. 3 is a block diagram of a software defect prediction system provided by another embodiment of the present invention. Referring to Fig. 3, the system 300 includes: a dimensionality reduction processing unit 310, an SVM training unit 320 and a defect prediction unit 330;

The dimensionality reduction processing unit 310 is used to perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, to obtain a low-dimensional vector in which each sample point in the first training data set is mapped to a low-dimensional space, and to obtain a low-dimensional vector obtained by each low-dimensional A second training data set composed of dimension vectors;

The SVM training unit 320 is used to train the support vector machine SVM classifier according to the second training data set, obtain the optimal classification hyperplane function of the SVM classifier, and then obtain the trained SVM classifier;

The defect prediction unit 330 is configured to perform defect prediction on the software to be predicted according to the trained SVM classifier. the

In one embodiment of the present invention, according to the local linear embedding algorithm LLE, the first training data set is subjected to dimensionality reduction processing, and the low-dimensional vectors in which each sample point in the first training data set is mapped to a low-dimensional space are obtained. The second training data set composed of low-dimensional vectors includes:

Let the first training data set be {X ₁ , X ₂ ,...,X _N }, X _i ∈ R ^D where X _i is a vector belonging to D-dimensional space;

Calculate the K nearest neighbor points of each sample point _Xi in the first training data set;

Use the K nearest neighbor points of each sample point to calculate the local reconstruction weight matrix W according to formula 1;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1

Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point _Xi using the j-th neighbor point, and the coefficients represented by all sample points _Xi in the first training data set using the neighbor point constitute the coefficient of all sample points Local reconstruction weight matrix W;

Calculate the corresponding low-dimensional vector of each sample point according to the obtained local reconstruction weight matrix W and its neighbor points according to formula 2;

$\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2

Wherein, I is the identity matrix, M=(IW) ^T (IW).

In one embodiment of the present invention, support vector machine SVM classifier is trained according to the second training data set, obtains the optimal classification hyperplane function of SVM classifier comprising:

Solve the optimal classification hyperplane function of the SVM classifier according to formula 3

$\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3

Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, _ξi is the slack variable, and φ(x) is the kernel function used by the SVM classifier.

In one embodiment of the present invention, the kernel function is a radial basis kernel function, in the form of:

$K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4

where σ is the width parameter of the radial basis kernel function. the

In one embodiment of the present invention, the SVM training unit is also used to optimize the parameter C of the SVM classifier and the parameter σ of the kernel function by using the grid search method and the ten-fold cross-validation method to find the highest classification accuracy of the SVM The value of the pair of parameters C and σ to determine the optimal classification hyperplane function of the SVM classifier. the

In one embodiment of the present invention, using the grid search method in conjunction with the ten-fold cross-validation method to optimize the parameter C of the SVM classifier and the kernel function parameter σ includes:

The parameters C and σ are selected by the grid search method; wherein, the value range of C is set to [2 ^-10 ,2 ⁷ ], and the value range of σ is set to [2 ^-10 ,2 ³ ]. The step size of the parameters is 0.1, and all combinations consisting of all values in the value range of C and all values in the value range of σ are obtained and searched.

In one embodiment of the present invention, using the grid search method in conjunction with the ten-fold cross-validation method to optimize the parameter C of the SVM classifier and the kernel function parameter σ also includes:

For each set of parameters C and σ selected, the classification accuracy rate under this set of parameter values is obtained, and the ten-fold crossover method is used for verification, and the set of parameters with the highest classification accuracy rate is taken as the best parameter value. Among them, The verification by using the ten-fold crossover method refers to dividing the second data set into 10 subsets, one subset is used as a test set, and the remaining 9 subsets are used as a training set to obtain a selected set of parameters. Classification accuracy rate, so repeated 10 times; get 10 classification accuracy rates under this group of parameters, use the average of these 10 classification accuracy rates as an index to evaluate the pros and cons of each group of parameters, and then compare the selected The average of the classification accuracy of the group parameters, and the group of parameters C and σ with the highest average are taken as the best parameter values. the

In one embodiment of the present invention, performing software defect prediction according to a trained SVM classifier includes:

Use the LLE algorithm to reduce the dimensionality of the data set of the forecasting software;

Input the data set after dimension reduction into the trained SVM classifier and judge it; if the input data falls into the space without defects determined by the optimal classification hyperplane function, it is determined that the software module corresponding to the data is not Contains defects and marks them in the output of the SVM classifier; if the input data falls into the defective space determined by the optimal classification hyperplane function, it is determined that the software module corresponding to the data contains defects and is included in the SVM classifier. mark in the output. the

It should be emphasized that the software defect prediction process of the software defect prediction system provided by the embodiment of the present invention can be summarized as the process of constructing a prediction model based on the LLE algorithm and the SVM classifier. The prediction model construction process mainly includes two modules, the first is dimensionality reduction processing, and the second is defect prediction. Among them, in the dimensionality reduction process, the training set used by the SVM classifier needs to be subjected to dimensionality reduction processing. At the same time, in practical applications, the test data set of the software to be tested also uses LLE dimensionality reduction processing, and then according to the dimensionality reduction data set And the obtained SVM optimal classification hyperplane function for specific prediction. This can ensure that the data set after dimension reduction can more fully reflect the data characteristics of the original data, thereby improving the accuracy of software defect prediction. the

The software defect prediction system provided by the embodiment of the present invention corresponds to the software defect prediction method described above. For the specific use process, refer to the relevant content in the foregoing method embodiments, and will not be repeated here. the

In summary, the software defect prediction method and software defect prediction system provided by the embodiments of the present invention use a local linear embedding algorithm to reduce the dimensionality of the training data set, so that the dimensionality-reduced data can more completely reflect the original According to the various characteristics of the data set, and according to the optimal classification hyperplane function of SVM, the optimal classification hyperplane function is used to predict software defects, so as to achieve the purpose of improving the accuracy of software defect prediction. the

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present invention are included in the protection scope of the present invention. the

Claims (16)

1. A software defect prediction method is characterized in that, comprising the following steps: Step 1. Perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, and obtain the low-dimensional vectors in which each sample point in the first training data set is mapped to the low-dimensional space, and obtain the first training data set composed of various low-dimensional vectors. Two training data sets; Step 2, the support vector machine SVM classifier is trained according to the second training data set, the optimal classification hyperplane function of the SVM classifier is obtained, and then the trained SVM classifier is obtained; Step 3, perform defect prediction on the software to be predicted according to the trained SVM classifier. 2. A kind of software defect prediction method as claimed in claim 1, is characterized in that, wherein in step 1, obtain the second training data set that is made up of each low-dimensional vector and adopt following method: 1.1 Let the first training data set be {X ₁ ,X ₂ ,...,X _N },X _i ∈R ^D , where X _i is a vector belonging to D-dimensional space; 1.2 Calculating the K nearest neighbor points of each sample point _Xi in the first training data set; 1.3 Use the K neighbor points of each sample point to calculate the local reconstruction weight matrix W according to formula 1; $\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1 Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point _Xi using the j-th neighbor point; all sample points _Xi in the first training data set use the coefficients represented by their neighbor points to form the local reconstruction weight value matrix W; 1.4 Calculate the low-dimensional vector corresponding to each sample point according to the obtained local reconstruction weight matrix W and the neighboring points of the sample point according to formula 2; $\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2 Wherein, I is the identity matrix, M=(IW) ^T (IW). 3. A kind of software defect prediction method as claimed in claim 1 or 2, is characterized in that, obtains the trained SVM classifier described in wherein step 2 and adopts following method: Solve the optimal classification hyperplane function of the SVM classifier according to formula 3 $\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3 Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, _ξi is the slack variable, and φ(x) is the kernel function used by the SVM classifier. 4. A kind of software defect prediction method as claimed in claim 3, is characterized in that, above-mentioned kernel function is radial basis kernel function, and the form is: $K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4 where σ is the width parameter of the radial basis kernel function. 5. a kind of software defect prediction method as claimed in claim 1 or 2 or 4 is characterized in that, in the above-mentioned optimal classification hyperplane function that obtains SVM classifier, adopt grid search method and ten-fold cross-validation method Optimize the parameter C of the SVM classifier and the parameter σ of the kernel function, and find the value of the pair of parameters C and σ that makes the SVM classification accuracy the highest, so as to determine the optimal classification hyperplane function of the SVM classifier. 6. A kind of software defect prediction method as claimed in claim 5, is characterized in that, above-mentioned employing grid search method and ten-fold cross-validation method carries out optimization to parameter C of SVM classifier and kernel function parameter σ comprising: Use the grid search method to value the parameters C and σ; get all the combinations of all the values in the range of C and all the values in the range of σ, and search. 7. A kind of software defect prediction method as claimed in claim 5, is characterized in that, above-mentioned employing grid search method and ten-fold cross-validation method carries out optimization to parameter C of SVM classifier and kernel function parameter σ comprising: For each set of parameters C and σ selected, the classification accuracy rate under this set of parameter values is obtained, and the ten-fold crossover method is used for verification, and the set of parameters with the highest classification accuracy rate is taken as the best parameter value; among them , using the ten-fold crossover method for verification means that the second data set is divided into 10 subsets, 1 subset is used as a test set, and the remaining 9 subsets are used as a training set to obtain 1 classification accuracy under a selected set of parameters. rate, repeating this 10 times; get 10 classification accuracy rates under this set of parameters, use the average of these 10 classification accuracy rates as an index to evaluate the pros and cons of each set of parameters, and then compare each set of selected parameters The average of the classification accuracy, the group of parameters C, σ with the highest average is taken as the best parameter value. 8. A kind of software defect prediction method as claimed in claim 1 or 2 or 4 or 6 or 7, is characterized in that, wherein carries out software defect prediction according to optimal classification hyperplane function and adopts following method: First, use the LLE algorithm to reduce the dimensionality of the data set of the forecasting software; Secondly, input the data set after dimension reduction into the trained SVM classifier and make a judgment; if the input data falls into the space without defects determined by the optimal classification hyperplane function, then Determine that the software module corresponding to the data does not contain a defect and mark it in the output result of the SVM classifier; if the input data falls into the defective space determined by the optimal classification hyperplane function, then determine that the The software modules corresponding to the above data contain defects and are marked in the output of the SVM classifier. 9. A software defect prediction system, comprising: a dimensionality reduction processing unit, an SVM training unit and a defect prediction unit; The dimensionality reduction processing unit is used to perform dimensionality reduction processing on the first training data set according to the local linear embedding algorithm LLE, to obtain a low-dimensional vector in which each sample point in the first training data set is mapped to a low-dimensional space, and to obtain a low-dimensional vector composed of each low-dimensional A second training data set composed of vectors; The SVM training unit is used to train the support vector machine SVM classifier according to the second training data set, and obtains the optimal classification hyperplane function of the SVM classifier, and then obtains the trained SVM classifier; the defect prediction unit is used for according to The trained SVM classifier performs defect prediction on the prediction software. 10. A kind of software defect prediction system as claimed in claim 9, is characterized in that, wherein obtaining the second training data set that is made up of each low-dimensional vector adopts the following method: 1.1 Let the first training data set be {X ₁ ,X ₂ ,...,X _N },X _i ∈R ^D , where X _i is a vector belonging to D-dimensional space; 1.2 Calculating the K nearest neighbor points of each sample point _Xi in the first training data set; 1.3 Use the K neighbor points of each sample point to calculate the local reconstruction weight matrix W according to formula 1; $\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2\\ \mathrm{the\; s}.t\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}=1\end{array}\right.$ Formula 1 Among them, N is the number of sample points, w _ij represents the coefficient represented by the i-th sample point _Xi using the j-th neighbor point; all sample points _Xi in the first training data set use the coefficients represented by their neighbor points to form the local reconstruction weight value matrix W; 1.4 Calculate the low-dimensional vector corresponding to each sample point according to the obtained local reconstruction weight matrix W and the neighboring points of the sample point according to formula 2; $\left\{\begin{array}{c}\min \mathrm{\ϵ}\left(w\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|Y_j-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{Y}_{\mathrm{ij}}\left|\right|}^2=\min \left({\mathrm{YMY}}^T\right)\\ \mathrm{the\; s}.t:{\mathrm{YY}}^T=I\end{array}\right.$ Formula 2 Wherein, I is the identity matrix, M=(IW) ^T (IW). 11. A kind of software defect prediction system as claimed in claim 9 or 10, it is characterized in that, wherein said obtained trained SVM classifier adopts the following method: Solve the optimal classification hyperplane function of the SVM classifier according to formula 3 $\left\{\begin{array}{c}\min \{\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\}\\ \mathrm{the\; s}.t.{\mathrm{the\; y}}_i({\mathrm{\ω}}^T\mathrm{\φ}\left(x_i\right)+b)\&Greater\; Equal;1-{\mathrm{\ξ}}_i,i=1,...,\mathrm{no}\end{array}\right.,{\mathrm{\ξ}}_i\&Greater\; Equal;0$ Formula 3 Among them, ω is a d-dimensional vector orthogonal to the classification hyperplane, b is the bias term, C is the penalty coefficient, _ξi is the slack variable, and φ(x) is the kernel function used by the SVM classifier. 12. A kind of software defect prediction system as claimed in claim 11, is characterized in that, above-mentioned kernel function is radial basis kernel function, and the form is: $K(x,x_i)=\exp \{-\frac{{|x-x_i|}^2}{{\mathrm{\σ}}^2}\}$ Formula 4 where σ is the width parameter of the radial basis kernel function. 13. A kind of software defect prediction system as claimed in claim 9 or 10 or 12, it is characterized in that, in the optimal classification hyperplane function of above-mentioned obtaining SVM classifier, adopt grid search method and ten-fold cross-validation method Optimize the parameter C of the SVM classifier and the parameter σ of the kernel function, and find the value of the pair of parameters C and σ that makes the SVM classification accuracy the highest, so as to determine the optimal classification hyperplane function of the SVM classifier. 14. A kind of software defect prediction system as claimed in claim 13, is characterized in that, above-mentioned employing grid search method and ten-fold cross-validation method carries out optimization to parameter C of SVM classifier and kernel function parameter σ comprising: Use the grid search method to value the parameters C and σ; get all the combinations of all the values in the range of C and all the values in the range of σ, and search. 15. A kind of software defect prediction system as claimed in claim 13, is characterized in that, above-mentioned employing grid search method and ten-fold cross-validation method carries out optimization to parameter C of SVM classifier and kernel function parameter σ comprising: For each set of parameters C and σ selected, the classification accuracy rate under this set of parameter values is obtained, and the ten-fold crossover method is used for verification, and the set of parameters with the highest classification accuracy rate is taken as the best parameter value; among them , using the ten-fold crossover method for verification means that the second data set is divided into 10 subsets, 1 subset is used as a test set, and the remaining 9 subsets are used as a training set to obtain 1 classification accuracy under a selected set of parameters. rate, repeating this 10 times; get 10 classification accuracy rates under this set of parameters, use the average of these 10 classification accuracy rates as an index to evaluate the pros and cons of each set of parameters, and then compare each set of selected parameters The average of the classification accuracy, the group of parameters C, σ with the highest average is taken as the best parameter value. 16. A kind of software defect prediction system as claimed in claim 9 or 10 or 12 or 14 or 15, it is characterized in that, wherein according to optimal classification hyperplane function, software defect prediction adopts the following method: First, use the LLE algorithm to reduce the dimensionality of the data set of the forecasting software; Secondly, input the data set after dimension reduction into the trained SVM classifier and make a judgment; if the input data falls into the space without defects determined by the optimal classification hyperplane function, then Determine that the software module corresponding to the data does not contain a defect and mark it in the output result of the SVM classifier; if the input data falls into the defective space determined by the optimal classification hyperplane function, then determine that the The software modules corresponding to the above data contain defects and are marked in the output of the SVM classifier.

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