  The challenge of describing model drift is an open question in unsupervised
learning. It can be difficult to evaluate at what point an unsupervised model
has deviated beyond what would be expected from a different sample from the
same population. This is particularly true for models without a probabilistic
interpretation. One such family of techniques, Topological Data Analysis, and
the Mapper algorithm in particular, has found use in a variety of fields, but
describing model drift for Mapper graphs is an understudied area as even
existing techniques for measuring distances between related constructs like
graphs or simplicial complexes fail to account for the fact that Mapper graphs
represent a combination of topological, metric, and density information. In
this paper, we develop an optimal transport based metric which we call the
Network Augmented Wasserstein Distance for evaluating distances between Mapper
graphs and demonstrate the value of the metric for model drift analysis by
using the metric to transform the model drift problem into an anomaly detection
problem over dynamic graphs.
