Search

In the era of big data, one of the key challenges is to discover process models and gain insights into business processes by analyzing event data recorded in information systems. However, Chaotic activity or infrequent behaviors often appear in actual event logs. Process models containing such behaviors are complex, difficult to understand, and hide the relevant key behaviors of the underlying processes. Established studies have generally achieved chaotic activity filtering by filtering infrequent activities or activities with high entropy values and ignoring the behavioral relationships that exist between activities, resulting in effective low-frequency behaviors being filtered. To solve this problem, this paper proposes an entropy-based behavioral closeness filtering of chaotic activities method. Firstly, based on the behavior profile theory of high-frequency logging activities, the process model is constructed by combining the feature network and the module network. Then, the identification of suspected chaotic activity sets is achieved through the Laplace entropy value. Next, a query model is built based on logs containing suspicious chaotic activity. Finally, based on the succession relationship, the behavioral closeness of the query model and the business process model is analyzed to achieve the goal of accurately filtering chaotic activities to retain behaviors beneficial to the process. To evaluate the performance of the method, we validated the effectiveness of the proposed algorithm in synthetic logs and real logs, respectively. Experimental results showed that the proposed method performs better in precision after filtering chaotic activities. [ABSTRACT FROM AUTHOR]

Process mining uses event logs to improve business processes, but such logs may contain privacy information. One popular research problem is the privacy protection of event logs. Publishing logs with differential privacy is one of major research directions. Existing research achieves privacy protection primarily by injecting random noise into event logs, or merging similar information. The former ignores the fact that injecting random noise will produce apparently unreasonable activity traces, and the latter will cause a loss of process information in the process mining perspective. To solve the above problems, this article proposes a differential algorithm based on randomized response to model Petri nets for the original event logs, select the important labels in the logs by the weak sequential relationship of control flow between activities, inject noise into the Petri net model based on the important labels using the randomized response approach, and establish a differential Petri net model. Experiments on public datasets show that the event logs produced by the approach proposed do not contain unreasonable traces. Compared with the baseline approach, the proposed approach performs better on Fitness metrics with consistent privacy requirements and retains more process variants, reducing the loss of original event log process information. [ABSTRACT FROM AUTHOR]

Let F q be a finite field of q elements, V an n-dimensional vector space over F q . Recently, Wang et al. in [Automorphisms and domination numbers of transformation graphs over vector spaces. Linear Multilinear Algebra. 2019;67:1350–1363] defined a graph Γ ′ (V) with vertex set T ∪ W , where T is the set of all nonzero singular linear transformations over V and W is the set of all nontrivial subspaces of V , and there is an undirected edge between A ∈ T and W ∈ W if and only if A maps W to the zero space, that is A (W) = { 0 }. In the end of Wang et al. [Automorphisms and domination numbers of transformation graphs over vector spaces. Linear Multilinear Algebra. 2019;67:1350–1363], the authors posed an open problem: Characterizing the domination number and the automorphisms of Γ ′ (V). In the present article, we solve this problem completely. [ABSTRACT FROM AUTHOR]