【正文】 construct aclassi175。er in this new space. We repeat this process toachieve a number of new classi175。ers. The dimensionalityof the new space is usually smaller than the original onein order to achieve further diversity between di174。erentnew spaces. Similar approach was used by Ho[50] forconstructing ensemble, where the random unit vectorsare enforced to be parallel to the basis of the originalspace.Table 1 presents the pseudo code of Rocus.We 175。rstly construct C classi175。ers from L by usingBagging[51] with the base learning algorithm A. Anylearning algorithm that incorporates certain randomness may be used to instantiate A. In this paper, Ainjects randomness by conducting random projectionbefore learning a classi175。er. In each semisupervisedlearning iteration, each classi175。er hi is re175。ned using thenewly labeled examples selected by H161。i, the ensembleTable 1. PseudoCode of the Rocus AlgorithmAlgorithm. RocusInput:the labeled set L, the unlabeled set U,the con175。dence threshold 181。, the minoritymajority ratio 176。,the number of individual classi175。ers C,the base learning algorithm A of the random mitteeProcess:1. Learn a random mittee fh1。 : : : 。 hCg from L usingBagging and the base learning algorithm A2. Repeat Steps 3187。9 until none of the classi175。er in therandom mittee changes3. Set t (t 2 N) as the current iteration number4. For each i 2 f1。 : : : 。Cg, do Steps 4187。95. Estimate error ei。t of H161。i on L6. Label all the unlabeled examples with H161。i7. Add the unlabeled examples whose labeling conn175。dence exceeds threshold 181。 to a newly labeledset L0i。t8. Undersample L0i。t such that the ratio of minorityclass over the majority class is no less than 176。9. If (3) holds, retrain hi from L [ L0i。t using thelearning algorithm AOutput: Compute H164。(x) according to (4)萬(wàn)方數(shù)據(jù)Yuan Jiang et al.: Software Defect Detection with Rocus 333of classi175。ers other than hi. Before the re175。nement,undersampling is employed to tailor the newly labeledset such that its minoritymajority ratio is roughly 176。.We use the condition in (3) as the stopping criterionof the iterative learning process. As holding a separatevalidation set is infeasible in semisupervised learningsettings, the error rate ^ei。t of H161。i is estimated on Lunder an assumption that the training data and testdata have the same distribution.Note that an alternative way to address the problems of \lack of su177。cient labeled data and \data imbalance simultaneously by imposing a \class proportionconstraint over a special type of base learner, which canadjust the portion of labeling of unlabeled data according to the constraint, just as what TSVM[31] does. However, such a strategy may exclude many good candidatebase learners that have good performance over someparticular defect detection problems but fail to adjusttheir labeling according to the constraints. In contrast,by incorporating undersampling, disagreementbasedsemisupervised learning method can be easily adaptedto the exploitation of unlabeled data while the data areimbalanced. Since the requirement of the base learnerin Rocus is no more than the ability of injecting randomness, which can be easily achieved, we may choosedi174。erent base learners according to speci175。c applicationscenario, and hence applicability of Rocus will be better.4 Empirical StudiesWe evaluate the e174。ectiveness of Rocus on eight software defect detection benchmark tasks. Each datasetcorresponds to di174。erent software projects in NASAMetrics Data Program[52]. Some of these softwareprojects are developed for satellite 176。ight control, whileothers are used for the groundsystem. All the software projects are written in C/C++. Each project consists of a number of software modules, each of whichis manually labeled as \defective if one or more defects were reported during the test phase and \defectfree otherwise. Typical software metrics such as LOCcounts, McCabe plexity measures derived from thepathway of modules, Halstead attributes measuring thenumber of operators and operands in the module asthe reading plexity, are extracted from each software module using some standard code analysis tools①.The detailed information of all the software metricsused in the current study can be found in [5]. Thedetailed information of the experimental datasets aretabulated in Table 2, where Ratio denotes the inverseof the minoritymajority ratio of the datasets. It is obvious from the table that the datasets are imbalancedand the number of defective modules are smaller thanthat of the modules without any defect.For each dataset, we randomly select 75% examplesfor training and keep the the remaining examples asidefor test. Since all the examples in the training set arelabeled, in order to simulate the case where only a smallportion of training data are labeled, we randomly partition the training set into labeled and unlabeled setsaccording to a labeled rate 185。. For example, if a training set consisting of 1000 examples and 185。 = 10%, 100examples are put into the labeled set with their labels,while the remaining 900 examples are put into the unlabeled set without their labels. In the experiment, weuse four di174。erent labeled rates: 10%, 20%, 30% and40%.In the experiments, the randomized base learner ofRocus is instantiated as an AdaBoost[53] precededby a random projector. The random projector 175。rst randomly generates 2d=3 random unit vectors and projectall the examples onto these random vectors. Here, d isthe number of features of the dataset. Following thesuggestions of [37], we 175。x the size of the random mittee to C = 6, and the con175。dence threshold 181。 is set to, which indicates an unlabeled example is regardedto be con175。dently labeled if more than 3=4 individualclassi175。ers of the random mittee agree on its labelin