# Detecting and Responding to Concept Drift in Business Processes
###### Abstract  
Concept drift, which refers to changes in the underlying process structure or customer behaviour over time, is inevitable in business processes, causing challenges in ensuring that the learned model is a proper representation of the new data. Due to factors such as seasonal effects and policy updates, concept drifts can occur in customer transitions and time spent throughout the process, either suddenly or gradually. In a concept drift context, we can discard the old data and retrain the model using new observations (sudden drift) or combine the old data with the new data to update the model (gradual drift) or maintain the model as unchanged (no drift). In this paper, we model a response to concept drift as a sequential decision making problem by combing a hierarchical Markov model and a Markov decision process (MDP). The approach can detect concept drift, retrain the model and update customer profiles automatically. We validate the proposed approach on 68 artificial datasets and a real-world hospital billing dataset, with experimental results showing promising performance. business process; concept drift; duration drift; hierarchical Markov model; Markov decision process +
Footnote †: journal: _Algorithms_  
0000-0001-9900-0000-0000-0000-0000-0000-0000-00000-0000-00  
publications took into account more than two perspectives such as time and resource. From a time perspective, concept drift is indicative of the variation in the time point when events occur, as described in [12]; however, it can also refer to changes in the time duration between events, which has not been well-investigated [3; 12]. To fill the research gap, this paper proposes a hierarchical Markov model-based Markov decision process (HMDP) method for modelling customer duration data, detecting concept drifts and automatically updating customer profiles. Businesses can gain benefits from automating their processes, such as saving employees' time, reducing costs and increasing efficiency [13], which is important in application areas, for example, for Test-Driven Data Analysis (TDDA) [14] and recommendation systems [15]. The idea of modelling the concept drift detection problem as a Markov decision process (MDP) originates from [PERSON] et al. 's work [16], which aims at solving feature-based supervised learning and distribution tracking problems. While in this paper, we concentrate on the PM context and propose a hierarchical Markov model (hierarchical MM) approach for process modelling. Specifically, in our previous work [17], we explored the possibility of detecting customer duration drift by using a semi-Markov process (SMP) model. In this paper, we applied it in our hierarchical MM (the bottom layer) and proposed a corresponding MDP stage to autonomously respond to concept drift. In the data modelling stage, the proposed HMDP approach represents customer behaviour using a two-layer hierarchical MM. The bottom layer is an SMP integrated with gamma mixture models to characterize customer transition probabilities and duration. The top layer, derived from the K-means clustering, is a high-level representation of the bottom layer customer behaviour. In the drift adaptation stage, the method first characterizes the old and new data separately using the hierarchical MM. The drift adaptation, i.e., customer profile updating problem, is then considered as an MDP. Specifically, the top-layer customer representations of the old and new data are combined as the MDP states where actions occur, i.e., keep (no drift), adapt (gradual drift) or retrain (sudden drift) the old hierarchical MM. This paper makes three main contributions. First, we represent the business process as a hierarchical MM, with customer activities and their duration as the bottom layer and customer performance patterns as the top layer. The aim of introducing the top layer is to reduce the difficulty of establishing the MDP model. Considering a process with \(n\) activities, the bottom layer representation (i.e., the SMP model) has \(n^{2}+(3m-1)*n^{2}\) parameters.