CN111625441A - Unsupervised heterogeneous defect prediction method based on geodesic flow kernel - Google Patents

Unsupervised heterogeneous defect prediction method based on geodesic flow kernel Download PDF

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CN111625441A
CN111625441A CN201910144409.3A CN201910144409A CN111625441A CN 111625441 A CN111625441 A CN 111625441A CN 201910144409 A CN201910144409 A CN 201910144409A CN 111625441 A CN111625441 A CN 111625441A
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姜淑娟
宫丽娜
姜丽
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China University of Mining and Technology CUMT
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Abstract

The invention relates to an unsupervised heterogeneous defect prediction method based on geodesic flow-type kernels, which comprises the following steps: (1) transforming the optimal subspace dimension; (2) constructing a geodesic flow; (3) calculating a geodesic flow kernel; (4) building a balanced data set; (5) and (5) building a prediction model. The method introduces the Grassmann manifold into unsupervised field adaptation, considers the project data sets of a source domain and a target domain as two points in the Grassmann manifold, then constructs a geodesic flow between the two points, integrates all the points on the path along the flow to construct a geodesic path, and realizes the spatial conversion from the source domain and the target domain. And finally, training a random forest by using the converted source domain data to construct a defect prediction model to predict the defect tendency of the target project.

Description

Unsupervised heterogeneous defect prediction method based on geodesic flow kernel
Technical Field
The invention belongs to the technical field of software testing, in particular to a method for assisting software testers in improving software reliability, which is used for accurately judging defective software modules in software testing.
Background
With the continuous improvement of software scale, software projects are more and more complex, the problem of software quality becomes a focus of attention, and software companies need to invest in larger manpower and material resources for software testing. The software defect prediction technology can find and lock defective modules in advance by means of a machine learning method in the early stage of software development, so that resources can be reasonably distributed, and the quality of software is ensured.
Most of the defect prediction technologies mainly focus on the problem of defect prediction of the same project, namely, a prediction model is built based on a large amount of labeled data of the same project to predict an unmarked software model of the same project. However, in actual project development, especially newly developed software projects, there are not enough sets of tagged data, resulting in difficult model training. Fortunately, there are many project data sets currently available from open sources that can be used to build models for prediction, i.e., cross-project defect prediction techniques.
Most of cross-project defect prediction technologies require that a source project and a target project have the same measurement element, and there are many random factors in software development, such as differences in programming habits, proficiency, application fields, and the like of developers, which all cause differences in measurement indexes, measurement granularity, and the like of software projects, so that there is a problem of differential measurement indexes in software projects of different companies or data sets of different software projects of the same company. To solve the problem of metric element difference, heterogeneous defect prediction is required. Heterogeneous defect prediction employs tag data sets with different metric elements to find defective modules of a target item. The geodesic flow type kernel method is an unsupervised field adaptation method for transfer learning, and a source domain mapping and a target domain are mapped to a public space through a feature mapping, so that the distance between the source domain and the target domain is minimum.
In addition, the characteristics of the software data sets, such as the intrinsic measurement attributes of the software, are different, resulting in relatively large data variance and relatively small data variance. Moreover, for the software project, the twenty-eight law is met, i.e. a defective software module is much smaller than a non-defective software module (class imbalance problem). The class imbalance problem can bias the classifier towards non-defective modules, failing to resolve defective models, and degrading the performance of the classifier. The sampling method can adopt a random over-sampling method or a random under-sampling method to enable the data set to reach the balance.
Disclosure of Invention
In order to solve the problem of difference between measurement elements of a source project (source domain) and a measured project (target domain) in heterogeneous defect prediction and reduce the difference between the source domain and the target domain, the invention introduces Grassmann manifold and provides an unsupervised domain adaptation method of a geodesic flow kernel. And (3) regarding the project data sets of the source domain and the target domain as two points in the Grassmann flow, then constructing a geodesic flow between the two points, and integrating all the points on the path along the flow to construct a geodesic path so as to realize the spatial conversion from the source domain and the target domain. And finally, training a random forest by using the converted source domain data to construct a defect prediction model to predict the defect tendency of the target project. Specifically, the method comprises the following steps:
1) an optimal subspace dimension transform is selected. The data in the source domain S and the target domain T are first normalized so that all data are in the same range. Then, the preprocessed data are respectively subjected to feature transformation on the combination of a source domain, a target domain and a source domain and a target domain by using a principal component analysis method, and the converted source domain P is respectively calculatedSAnd a target domain PTTo the merged domain PS+TIs included angle of space
Figure 510312DEST_PATH_IMAGE001
And
Figure 948247DEST_PATH_IMAGE002
minimization by greedy algorithm
Figure 306547DEST_PATH_IMAGE003
Finally, the optimal subspace dimension d of the principal component analysis is determined, so that the transformed feature set PSAnd PTIt is possible to express main information within the respective domains with the distance between the source domain and the target domain being minimized.
2) And constructing a geodesic line. Assuming the feature space P of the source domain and the target domain obtained in the step 1)SAnd PTMapping functions in the flow space by geodesic lines
Figure 779117DEST_PATH_IMAGE004
After mapping, at both poles 0 and 1, i.e.
Figure 502353DEST_PATH_IMAGE005
,
Figure 427584DEST_PATH_IMAGE006
. For a point t between two points from the source domain to the target domain in the manifold, the function value of the geodesic function can be expressed as:
Figure 586645DEST_PATH_IMAGE007
. In the formula, in the above-mentioned formula,
Figure 913721DEST_PATH_IMAGE008
is composed of
Figure 135755DEST_PATH_IMAGE009
The complement of (1), the dimension of which is D-D and satisfies
Figure 548282DEST_PATH_IMAGE010
And = 0. To is pair
Figure 310702DEST_PATH_IMAGE011
Performing singular value conversion to obtain
Figure 367650DEST_PATH_IMAGE012
、
Figure 822903DEST_PATH_IMAGE013
、
Figure 660409DEST_PATH_IMAGE014
And
Figure 226519DEST_PATH_IMAGE015
namely:
Figure 200291DEST_PATH_IMAGE016
,
Figure 826445DEST_PATH_IMAGE017
3) and calculating a geodesic flow kernel. For smooth movement of the source domain to the target domain, the source domain is targeted
Figure 151247DEST_PATH_IMAGE018
And a target domain
Figure 255469DEST_PATH_IMAGE019
Calculate them by the idea of integration in
Figure 411644DEST_PATH_IMAGE020
Up-projection to an infinite-dimensional vector, the geodesic flow kernel is defined using the two infinite-dimensional projections, namely:
Figure DEST_PATH_IMAGE021
where G is a semi-positive definite matrix. The expression form of G is:
Figure 146382DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE023
,
Figure 689971DEST_PATH_IMAGE024
and
Figure 801147DEST_PATH_IMAGE025
is a diagonal matrix, the elements of which are calculated as:
Figure 811828DEST_PATH_IMAGE026
,
Figure 717467DEST_PATH_IMAGE027
Figure 813599DEST_PATH_IMAGE028
is composed of
Figure 197307DEST_PATH_IMAGE029
And
Figure 328074DEST_PATH_IMAGE030
the included angle of the space between the two.
4) An equilibrium data set is established. And aiming at the G obtained in the step 3), the source domain and the target domain are transferred to the corresponding common space. And aiming at the condition that the number of defective examples in the source domain data is more than that of non-defective examples, sampling the defective examples by adopting a random oversampling method to obtain a data-balanced source domain data set.
5) And establishing a prediction model. And 4) establishing a classifier on the converted source domain data by using a random forest method according to the source domain data and the target domain data obtained in the step 4), predicting all samples of the target domain, and obtaining a result to calculate a corresponding performance evaluation index.
Further, the specific steps of the step 1) are as follows:
step 1) -1: a start state;
step 1) -2: respectively carrying out principal component analysis on the source domain data set S, the target domain data set T and the combined set S + T to obtain
Figure 466931DEST_PATH_IMAGE009
、
Figure 988042DEST_PATH_IMAGE030
And
Figure 237758DEST_PATH_IMAGE031
；
step 1) -3: computing
Figure 160715DEST_PATH_IMAGE009
And
Figure 470473DEST_PATH_IMAGE031
included angle of space of
Figure 102050DEST_PATH_IMAGE001
And
Figure 93139DEST_PATH_IMAGE030
and
Figure 870603DEST_PATH_IMAGE031
included angle of space of
Figure 351262DEST_PATH_IMAGE032
Thereby obtaining
Figure 581387DEST_PATH_IMAGE003
；
Step 1) -4: repeating the steps 2 and 3 by adopting a greedy algorithm, thereby determining the optimal d;
step 1) -5: and finishing the dimension transformation of the optimal subspace.
Further, the specific steps of the step 2) are as follows:
step 2) -1: a start state;
step 2) -2: for the products obtained according to step 1)
Figure 396675DEST_PATH_IMAGE009
Calculating
Figure 90962DEST_PATH_IMAGE009
Is not limited to
Figure 680206DEST_PATH_IMAGE033
Satisfy the following requirements
Figure 725522DEST_PATH_IMAGE010
=0；
Step 2) -3: decomposing by using kiwi fruit (SVG) method
Figure 58415DEST_PATH_IMAGE034
And
Figure 607208DEST_PATH_IMAGE035
to obtain
Figure 632933DEST_PATH_IMAGE012
、
Figure 899966DEST_PATH_IMAGE013
、
Figure 770970DEST_PATH_IMAGE014
And
Figure 439849DEST_PATH_IMAGE015
；
step 2) -4: according to obtaining
Figure 636475DEST_PATH_IMAGE012
、
Figure 62908DEST_PATH_IMAGE013
、
Figure 3182DEST_PATH_IMAGE014
And
Figure 526567DEST_PATH_IMAGE015
building a geodesic flow
Figure 625586DEST_PATH_IMAGE020
Step 2) -5: and finishing the construction of the geodesic flow.
Further, the specific steps of the step 3) are as follows:
step 3) -1: a start state;
step 3) -2: computing
Figure 804895DEST_PATH_IMAGE009
And
Figure 283280DEST_PATH_IMAGE036
included angle of space of
Figure 661172DEST_PATH_IMAGE037
；
Wherein
Figure 199601DEST_PATH_IMAGE038
Step 3) -3: according to
Figure 662943DEST_PATH_IMAGE037
Computing
Figure 945020DEST_PATH_IMAGE039
；
Step 3) -4: final calculation
Figure 442997DEST_PATH_IMAGE040
；
Step 3) -5: and finishing the geodesic flow core calculation.
Further, the specific steps of the step 4) are as follows:
step 4) -1: a start state;
step 4) -2: by using
Figure 886748DEST_PATH_IMAGE041
Obtaining a transformed source domain
Figure 102966DEST_PATH_IMAGE042
And a target domain
Figure 923154DEST_PATH_IMAGE043
；
Step 4) -3: after conversion
Figure 275638DEST_PATH_IMAGE042
Random oversampling to obtain as many defective instances as non-defective ones
Step 4) -4: balanced source domain data set
Figure 890290DEST_PATH_IMAGE042
And (5) finishing construction.
Further, the specific steps of the step 5) are as follows:
step 5) -1: a start state;
step 5) -2: computingObtained according to step 4)
Figure 328225DEST_PATH_IMAGE042
Training a random forest classifier to obtain a training model;
step 5) -3: targeting domains using trained models
Figure 949175DEST_PATH_IMAGE043
And (6) performing prediction.
Step 5) -4: and finishing the establishment of the prediction model.
The invention discloses an unsupervised heterogeneous defect prediction method based on geodesic flow type kernel, which introduces Grassman manifold into unsupervised field adaptation, considers project data sets of a source domain and a target domain as two points in the Grassman manifold, then constructs a geodesic flow between the two points, integrates all the points on the path along the flow to construct a geodesic path, and realizes the spatial conversion from the source domain and the target domain. And finally, training a random forest by using the converted source domain data to construct a defect prediction model to predict the defect tendency of the target project. The method greatly improves the accuracy of prediction, enables software testers to reasonably distribute human and material resources, and improves the working efficiency of software testing, thereby effectively controlling the quality of software projects.
Drawings
Fig. 1 is a flowchart of an unsupervised heterogeneous defect prediction method based on a geodesic flow kernel in the implementation of the present invention.
Fig. 2 is a flow chart of the optimal subspace dimension transformation of fig. 1.
Fig. 3 is a flow chart of the geodesic construction of fig. 1.
Fig. 4 is a flow chart of the geodesic flow kernel calculation of fig. 1.
FIG. 5 is a flow chart of the balanced data set construction of FIG. 1.
FIG. 6 is a flow chart of the predictive model construction of FIG. 1.
Detailed Description
To further illustrate the technical content of the present invention, specific examples are described below with reference to the accompanying drawings.
Fig. 1 is a flowchart of an unsupervised heterogeneous defect prediction method based on a geodesic core according to an embodiment of the present invention.
An unsupervised heterogeneous defect prediction method based on geodesic flow kernel is characterized by comprising the following steps:
and S1, performing optimal subspace dimension transformation, and finding an optimal principal component analysis subspace d by using a greedy algorithm, so that the source domain and the target domain keep the maximum consistency under the d-dimensional subspace.
S2 geodesic flow construction, and according to the optimal subspace dimension d obtained by S1 construction, performing principal component analysis on the source domain and the target domain to obtain
Figure 156165DEST_PATH_IMAGE009
And
Figure 207298DEST_PATH_IMAGE036
introducing a Grassmann manifold,
Figure 70211DEST_PATH_IMAGE009
and
Figure 294519DEST_PATH_IMAGE036
respectively mapping to two poles of 0 and 1, thereby obtaining the geodesic function of [0,1]A function value of a point t in between.
S3, calculating a geodesic flow kernel, obtaining the projection of the source domain vector and the target domain vector on the geodesic function by adopting the integral idea according to the geodesic function at the t obtained in S2, and defining the geodesic flow kernel according to the inner product of the projection.
S4 balance data set construction, converting the source domain and the target domain to a public space according to the G obtained in S3, copying a defective example of the converted source domain by adopting a random oversampling method, and balancing the defective example.
And S5 prediction model construction, namely obtaining balanced source domain label data according to S4, training a random forest classifier to obtain a prediction model with better performance, and predicting target domain data obtained in S4.
FIG. 2 is a flow chart of an optimal subspace dimension transformation. And finding the optimal principal component analysis subspace d by using a greedy algorithm. The method comprises the following specific steps.
Step 1: a start state; step 2: performing principal component analysis on the source domain, the target domain and the collection domain; and step 3: calculating included angles from the source domain and the target domain to the collection; and 4, step 4: obtaining an optimal subspace dimension d by adopting a greedy algorithm; and 5: and finishing the construction of the geodesic flow.
Fig. 3 is a flow chart of geodesic construction. And aiming at the obtained optimal subspace, introducing a Grassmann manifold to obtain a geodesic flow function. The method comprises the following specific steps.
Step 1: a start state; step 2: obtained
Figure 496962DEST_PATH_IMAGE009
Is not limited to
Figure 718996DEST_PATH_IMAGE044
(ii) a And step 3: decomposition by SVG
Figure 865943DEST_PATH_IMAGE034
And
Figure 831625DEST_PATH_IMAGE035
(ii) a And 4, step 4: constructing a geodesic flow function; and 5: and finishing the construction of the geodesic flow.
FIG. 4 is a flow chart of computing a geodesic core. And calculating the geodesic current core by adopting an integral idea according to the geodesic function. The method comprises the following specific steps.
Step 1: a start state; step 2: calculating a space included angle; and step 3: calculating a matrix according to the included angle; and 4, step 4: calculating to obtain a geodesic current core; and 5: and finishing the geodesic current type nuclear calculation.
FIG. 5 is a flow chart of balanced data set construction. And sampling the source domain data by using a random oversampling method according to the geodesic flow type nuclear conversion source domain and the target domain. The method comprises the following specific steps.
Step 1: a start state; step 2: converting a source domain and a target domain; and step 3: randomly over-sampling source domain data; and 4, step 4: and finishing the construction of the balance data set.
FIG. 6 is a flow chart of predictive model construction. And training a random forest classifier according to the balanced source domain data set, and predicting a sample of the target domain by using the trained model. The method comprises the following specific steps.
Step 1: a start state; step 2: training a random forest classifier; and step 3: predicting a target domain instance; and 4, step 4: and providing the prediction result for a tester to perform test resource allocation.
In conclusion, the invention solves the problems of isomerism and class imbalance in defect prediction, not only improves the discovery of defect modules, but also improves the efficiency of software testing.

Claims (6)

1. An unsupervised heterogeneous defect prediction method based on geodesic flow type kernel is characterized in that a source domain project and a target domain project are regarded as two points in a Grassman flow, the geodesic flow is constructed, and the conversion from a source domain to a target domain space is realized; secondly, carrying out balance processing on the source domain project data by using a random over-adoption technology, and constructing a defect prediction model by combining a random forest method of machine learning to realize classification of the target project module; the method comprises the following steps:
1) selecting optimal subspace dimension transformation;
definition 1: the distance between the source domain and the target domain is expressed as the total measurement of the spatial included angle between the source domain and the merged domain, and the calculation formula is as follows:
Figure FDA0001979543460000011
merging the domains: a principal component analysis set of a merged set of source and target domains;
αd: the included angle between the d subspace and the merging domain after the source domain principal component analysis;
βd: the included angle between the d subspace and the merged domain space after the principal component analysis of the target domain;
finding an optimal principal component analysis subspace d by using a greedy algorithm, so that the source domain and the target domain keep the maximum consistency under the d-dimensional subspace;
2) constructing a geodesic line;
definition 1: the function value of the geodesic function at point t can be expressed as:
Figure FDA0001979543460000012
Figure FDA0001979543460000013
a geodesic mapping function is applied to the geodesic,
Figure FDA0001979543460000014
using the optimal subspace dimension d obtained in the step 1), carrying out principal component analysis on the source domain and the target domain to obtain PSAnd PTIntroduction of the Grassmann manifold, PSAnd PTRespectively mapping to two poles of 0 and 1, thereby obtaining the geodesic function of [0,1]A function value of a point t in between;
3) calculating a geodesic flow kernel;
definition 1: the geodesic flow kernel is defined using the two infinite-dimensional projections, namely:
Figure FDA0001979543460000015
wherein G is a semi-positive definite matrix, and the expression form of G is as follows:
Figure FDA0001979543460000016
Λ1,Λ2and Λ3Is a diagonal matrix, the elements of which are calculated as:
Figure FDA0001979543460000017
θiis PsAnd PTThe spatial included angle between the two parts;
using the geodesic function at the position t obtained in the step 2), adopting the integral idea to obtain the projection of the source domain vector and the target domain vector on the geodesic function, and defining a geodesic flow kernel according to the inner product of the projection;
4) establishing a balanced data set; using the G obtained in the step 3), transferring the source domain and the target domain to a corresponding common space, and sampling the defective examples by adopting a random oversampling method aiming at the condition that the defective examples in the source domain data are more than the non-defective examples to obtain a data-balanced source domain data set;
5) establishing a prediction model, using the source domain and target domain data obtained in the step 4), establishing a classifier on the converted source domain data by using a random forest method of machine learning, predicting all samples of the target domain, and obtaining a result to calculate a corresponding performance evaluation index.
2. The method for unsupervised heterogeneous defect prediction based on geodesic flow kernels according to claim 1, characterized in that in step 1) an optimal subspace dimension transformation is selected; and finding an optimal principal component analysis subspace d by using a greedy algorithm, so that the source domain and the target domain keep the maximum consistency under the d-dimensional subspace.
3. The unsupervised heterogeneous defect prediction method based on geodesic flow kernel of claim 1, characterized in that in step 2) geodesic lines are constructed; the source domain and target domain project data sets are considered as two points in a grassmann flow, and then a geodesic flow is constructed between the two points.
4. The unsupervised heterogeneous defect prediction method based on geodesic kernels according to claim 1, characterized in that in step 3) geodesic kernels are calculated; the method comprises the following specific steps: and (3) using the geodesic function at the position of the geodesic flow t, adopting the integral idea to obtain the projection of the vector of the source domain and the target domain on the geodesic function, and defining a geodesic flow kernel according to the inner product of the projection.
5. The method for unsupervised heterogeneous defect prediction based on geodesic flow kernels according to claim 1, characterized in that in step 4) a balanced dataset is established; the method comprises the following specific steps: and transferring the source domain and the target domain to a corresponding common space, and sampling the defective examples by adopting a random oversampling method aiming at the condition that the defective examples in the source domain data are more than the non-defective examples to obtain a data-balanced source domain data set.
6. The geodesic flow kernel based unsupervised heterogeneous defect prediction method of claim 1, characterized in that in step 5) a prediction model is established; and establishing a classifier on the converted source domain data by using a random forest method of machine learning, predicting all samples of the target domain, and calculating corresponding performance evaluation indexes according to results.
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