Abstract
A novel method to cluster event log traces is presented in this paper. In contrast to the approaches in the literature, the clustering approach of this paper assumes an additional input: a process model that describes the current process. The core idea of the algorithm is to use model traces as centroids of the clusters detected, computed from a generalization of the notion of alignment. This way, model explanations of observed behavior are the driving force to compute the clusters, instead of current model agnostic approaches, e.g., which group log traces merely on their vector-space similarity. We believe alignment-based trace clustering provides results more useful for stakeholders. Moreover, in case of log incompleteness, noisy logs or concept drift, they can be more robust for dealing with highly deviating traces. The technique of this paper can be combined with any clustering technique to provide model explanations to the clusters computed. The proposed technique relies on encoding the individual alignment problems into the (pseudo-)Boolean domain, and has been implemented in our tool DarkSider that uses an open-source solver.
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Notes
- 1.
Operators ; and || denote sequential and parallel composition, respectively.
- 2.
We understand the \(\sum \) as a sum over a multiset, taking multiplicities into account. For instance, with the multiset \(A = \{1, 1\}\), we get \(\sum _{i \in A}i = 2\).
- 3.
More precisely, the problem of existence of a \(\delta \)-multi-alignment for given \(\mathcal {C}\), \(N\) and \(\delta \) (represented in unary), is NP-complete. For NP-hardness, we use a reduction from the problem of reachability of a marking \(m\) in a 1-safe acyclic Petri net \(N\), known to be NP-complete [12, 13], to the existence of a \(0\)-multi-alignment with the empty collection \(\mathcal C = \emptyset \).
- 4.
Pseudo-Boolean constraints are generalizations of Boolean constraints. They allow one to specify constant bounds on the number of variables which can/must be assigned to true among a set \(V\) of variables. We write them as \(a\,\le \,\sum _{v\,\in \,V}v\, \le \,b\). Pseudo-Boolean constraints are not more expressive but can be upto exponentially more concise than Boolean constraints. Some pseudo-Boolean solvers also offer to search for a solution minimizing a pseudo-Boolean objective of the same form \(\sum _{v\,\in \,V}v\): number of variables assigned to true among \(V\).
- 5.
This holds as well for Hamming or edit distance.
- 6.
For efficiency reasons, DarkSideruses currently an ad-hoc distance intermediate between Hamming and Levenshtein.
- 7.
If more flexible distance parameters are applied, a clustering with only 10 traces unclustered can be computed.
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Acknowledgements
We thank Bart Hompes for facilitating the clustering results of his tool for the example used in the experiments. This work has been partially supported by funds from the Spanish Ministry for Economy and Competitiveness (MINECO), the European Union (FEDER funds) under grant COMMAS (ref. TIN2013-46181-C2-1-R).
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Chatain, T., Carmona, J., van Dongen, B. (2017). Alignment-Based Trace Clustering. In: Mayr, H., Guizzardi, G., Ma, H., Pastor, O. (eds) Conceptual Modeling. ER 2017. Lecture Notes in Computer Science(), vol 10650. Springer, Cham. https://doi.org/10.1007/978-3-319-69904-2_24
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