An Approach For Verifying And Validating Clustering Based Anomaly Detection Systems Using Metamorphic Testing

An oracle or test oracle is a mechanism that a software tester uses to verify the program output. In software testing, the oracle problem arises when either the oracle is not available or it may be available but is so expensive that it is infeasible to apply. To help address this problem in testing machine learning-based applications, we propose an approach for testing clustering algorithms. We exemplify this in the implementation of the award-winning density-based clustering algorithm i.e., Density-based Spatial Clustering of Applications with Noise (DBSCAN). Our proposed approach is based on the 'Metamorphic Testing' technique which is considered an effective approach in alleviating the oracle problem. Our contributions in this paper include, i) proposing and showing the applicability of a broader set of 21 Metamorphic Relations (MRs), among which 8 target the verification aspect, whereas, 14 of them target the validation aspect of testing the algorithm under test, and ii) identifying and segregating the MRs (by providing a detailed analysis) to help both naive and expert users understand how the proposed MRs target both the verification and validation aspects of testing the DBSCAN algorithm. To show the effectiveness of the proposed approach, we further conduct a case study on an anomaly detection system. The results obtained show that, i) different MRs have the ability to reveal different violation rates (for the given data instances); thus, showing their effectiveness, and ii) although we have not found any implementation issues (through verification) in the algorithm under test (that further enhances our trust in the implementation), the results suggest that the DBSCAN algorithm may not be suitable for scenarios (meeting the user expectations a.k.a validation) captured by almost 79% of violated MRs; which show high susceptibility to small changes in the dataset.