Quotients for Behaviour Comparisons: Monotone Precision and Recall Measures for Process Mining.

The behavioural comparison of dynamic systems is an im-portant concern of information systems research, sociology, managementscience and software engineering. In the area of process mining, varioustechniques for conformance checking have been proposed to measure howsimilar observed execution sequences and system specification such givenby a business process models are. Though various measures have beenproposed, [2] observe that non of them fulfills essential properties. Toaddress this research problem, we build on the observation that if twosystems are not language-equivalent, the quantification of behaviouraldifferences enables conclusions on the extent of the deviation. However,there is no systematic approach for defining quotients and it is unclearwhich measures enable meaningful comparisons of systems having infi-nite behaviours.It is the contribution of this talk to introduce a framework for defininglanguage quotients, which resolves the measurement problem of confor-mance checking in process mining. We instantiate the framework withcardinality- and entropy-based measures to handle finite and infinite be-haviours, and prove important properties of the quotients. We demon-strate the application of quotients in the field of process mining to cap-ture precision and recall between a log of recorded and a model of ex-pected system executions. An experimental evaluation of the quotientsusing our open-source implementation demonstrates their feasibility andindicates that the quotients enable a monotonic assessment, unlike state-of-the-art measures in process mining. This talk is based on joint researchwith Polyvyanyy, Solti, Weidlich, and Di Ciccio [1]