Local Process Model (LPM) discovery is focused on the mining of a set of process models where each model describes the behavior represented in the event log only partially, i.e. subsets of possible events are taken into account to create so-called local process models. Often such smaller models provide valuable insights into the behavior of the process, especially when no adequate and comprehensible single overall process model exists that is able to describe the traces of the process from start to end. The practical application of LPM discovery is however hindered by computational issues in the case of logs with many activities (problems may already occur when there are more than 17 unique activities). In this paper, we explore three heuristics to discover subsets of activities that lead to useful log projections with the goal of speeding up LPM discovery considerably while still finding high-quality LPMs. We found that a Markov clustering approach to create projection sets results in the largest improvement of execution time, with discovered LPMs still being better than with the use of randomly generated activity sets of the same size. Another heuristic, based on log entropy, yields a more moderate speedup, but enables the discovery of higher quality LPMs. The third heuristic, based on the relative information gain, shows unstable performance: for some data sets the speedup and LPM quality are higher than with the log entropy based method, while for other data sets there is no speedup at all.
The goal of Process Mining is to extract process models from logs of a system. Among the possible models to represent a process, Petri nets is an ideal candidate due to its graphical representation, clear semantics and expressive power. The theory of regions can be used to transform a log into a Petri net, but unfortunately the transformation requires algorithms with high complexity. This paper provides techniques to overcome this limitation. Either by using decomposition techniques, or by clustering events in the log and working on projections, the proposed approach can be used to widen the applicability of classical region-based techniques. Traces are everywhere from information systems that store their continuous executions, to any type of health care applications that record each patient's history. The transformation of a set of traces into a mathematical model that can be used for a formal reasoning is therefore of great value. The discovery of process models out of traces is an interesting problem that has received significant attention in the last years. This is a central problem in Process Mining, a novel area which tries to close the cycle between system design and validation, by resorting on methods for the automated discovery, analysis and extension of process models. In this work, algorithms for the derivation of a Petri net from a set of traces are presented. The methods are grounded on the theory of regions, which maps a model in the state-based domain (e.g., an automata) into a model in the event-based domain (e.g., a Petri net). When dealing with large examples, a direct application of the theory of regions will suffer from two problems: one is the state-explosion problem, i.e., the resources required by algorithms that work at the state-level are sometimes prohibitive. This paper introduces decomposition and projection techniques to alleviate the complexity of the region-based algorithms for Petri net discovery, thus extending its applicability to handle large inputs. A second problem is known as the overfitting problem for region-based approaches, which informally means that, in order to represent with high accuracy the trace set, the models obtained are often spaghetti-like. By focusing on special type of processes called conservative and for which an elegant theory and efficient algorithms can be devised, the techniques presented in this paper alleviate the overfitting problem and moreover incorporate structure into the models generated.