Entropy as a Measure of Log Variability

Process mining algorithms fall in two classes: imperative miners output flow diagrams, showing all possible paths, whereas declarative miners output constraints, showing the rules governing a process. But given a log, how do we know which of the two to apply? Assuming that logs exhibiting a large degree of variability are more suited for declarative miners, we can attempt to answer this question by defining a suitable measure of the variability of the log. This paper reports on an exploratory study into the use of entropy measures as metrics of variability. We survey notions of entropy used, e.g. in physics; we propose variant notions likely more suitable for the field of process mining; we provide an implementation of every entropy notion discussed; and we report entropy measures for a collection of both synthetic and real-life logs. Finally, based on anecdotal indications of which logs are better suited for declarative/imperative mining, we identify the most promising measures for future studies. For estimating overall entropy, global block and k-nearest neighbour estimators of entropy appear most promising and excel at identifying noise in logs. For estimating entropy rate we identify Lempel–Ziv and certain variants of k-block estimators performing well, and note that the former is more stable, but sensitive to noise, while the latter is less stable, being sensitive to cut-off constraints determining block size.