  It is common practice of the outlier mining community to repurpose
classification datasets toward evaluating various detection models. To that
end, often a binary classification dataset is used, where samples from one of
the classes is designated as the inlier samples, and the other class is
substantially down-sampled to create the ground-truth outlier samples.
Graph-level outlier detection (GLOD) is rarely studied but has many potentially
influential real-world applications. In this study, we identify an intriguing
issue with repurposing graph classification datasets for GLOD. We find that
ROC-AUC performance of the models changes significantly (flips from high to
very low, even worse than random) depending on which class is down-sampled.
Interestingly, ROC-AUCs on these two variants approximately sum to 1 and their
performance gap is amplified with increasing propagations for a certain family
of propagation based outlier detection models. We carefully study the graph
embedding space produced by propagation based models and find two driving
factors: (1) disparity between within-class densities which is amplified by
propagation, and (2)overlapping support (mixing of embeddings) across classes.
We also study other graph embedding methods and downstream outlier detectors,
and find that the intriguing performance flip issue still widely exists but
which version of the downsample achieves higher performance may vary.
Thoughtful analysis over comprehensive results further deeper our understanding
of the established issue.
