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In machine learning, supervised classifiers are used to obtain predictions for unlabeled data by inferring prediction functions using labeled data. Supervised classifiers are widely applied in domains such as computational biology, computational physics and healthcare to make critical decisions. However, it is often hard to test supervised classifiers since the expected answers are unknown. This is commonly known as the oracle problem and metamorphic testing (MT) has been used to test such programs. In MT, metamorphic relations (MRs) are developed from intrinsic characteristics of the software under test (SUT). These MRs are used to generate test data and to verify the correctness of the test results without the presence of a test oracle. Effectiveness of MT heavily depends on the MRs used for testing. In this paper we have conducted an extensive empirical study to evaluate the fault detection effectiveness of MRs that have been used in multiple previous studies to test supervised classifiers. Our study uses a total of 709 reachable mutants generated by multiple mutation engines and uses data sets with varying characteristics to test the SUT. Our results reveal that only 14.8% of these mutants are detected using the MRs and that the fault detection effectiveness of these MRs do not scale with the increased number of mutants when compared to what was reported in previous studies. 

Metamorphic testing is a well known approach to tackle the oracle problem in software testing. This technique requires the use of source test cases that serve as seeds for the generation of follow-up test cases. Systematic design of test cases is crucial for the test quality. Thus, source test case generation strategy can make a big impact on the fault detection effectiveness of metamorphic testing. Most of the previous studies on metamorphic testing have used either random test data or existing test cases as source test cases. There has been limited research done on systematic source test case generation for metamorphic testing. This paper provides a comprehensive evaluation on the impact of source test case generation techniques on the fault finding effectiveness of metamorphic testing. We evaluated the effectiveness of line coverage, branch coverage, weak mutation and random test generation strategies for source test case generation. The experiments are conducted with 77 methods from 4 open source code repositories. Our results show that by systematically creating source test cases, we can significantly increase the fault finding effectiveness of metamorphic testing. Further, in this paper we introduce a simple metamorphic testing tool called "METtester" that we use to conduct metamorphic testing on these methods.