  Comparing business process variants using event logs is a common use case in
process mining. Existing techniques for process variant analysis detect
statistically-significant differences between variants at the level of
individual entities (such as process activities) and their relationships (e.g.
directly-follows relations between activities). This may lead to a
proliferation of differences due to the low level of granularity in which such
differences are captured. This paper presents a novel approach to detect
statistically-significant differences between variants at the level of entire
process traces (i.e. sequences of directly-follows relations). The cornerstone
of this approach is a technique to learn a directly follows graph called mutual
fingerprint from the event logs of the two variants. A mutual fingerprint is a
lossless encoding of a set of traces and their duration using discrete wavelet
transformation. This structure facilitates the understanding of statistical
differences along the control-flow and performance dimensions. The approach has
been evaluated using real-life event logs against two baselines. The results
show that at a trace level, the baselines cannot always reveal the differences
discovered by our approach, or can detect spurious differences.
