HMMs in process mining literature

Although hidden Markov models (HMMs) have been widely used in various domains such as bioinformatics, speech recognition and handwriting recognition for handling sequences, there is a limited number of research that has applied HMMs in process mining. According to Rojas et al. [19], only 4% of healthcare process mining techniques have been done by HMMs. In this section we aim to present how HMMs have been employed in process mining field.

Peters et al.[79] and Poelmans et al. [80] used a hybrid method consists of data discovery technique such as formal concept analysis (FCA) and Hidden Markov model. The aim of using FCA is to extract semantic information about different patients clusters and then feed these clusters to the available Matlab toolbox HMM model for process discovery.

This approach has achieved good results in [80] for finding exceptions care flow in each clus- ter and simplifying correlation analysis between length of stay in hospital and some missing treatment practise. Also, in [79] this hybrid method found some process improvements sugges- tions. However, the adopted method had a priori separation of process into different clusters before process discovery step and consequently, the results are highly affected by the validity of clustering method. Also, discovering the mainstream process model is not applicable using this method.

Carrera & Jung [81] have utilized a HMM to model resources workflow and improve resources allocation. The novelty of this work comes from combining organizational, control-flow and probabilistic perspectives in one process model.

HMM parameters were initialized manually not randomly by constructing footprint matrix with frequencies for observations, where observations here are the resources names, and states, which represent events. Initial transition probability was created based on a dummy start/end obser- vation. The algorithm of Expectation-Maximisation was used to learn the hidden structure of resource workflow. Results showed that HMM can be used to model resources workflow and

consequently improve managing resources allocation and avoiding overload.

Rozinat et al. [82] have employed HMM to measure the quality of process model. This work was motivated by the need for finding new evaluation metrics for process model to measure what is beyond the ability for replying process instances such as noise resistance and incompleteness. A Petri net model was constructed and each labelled tasks on that model is mapped to a hid- den state on HMM. The experiment aimed to gradually inject noise to several event logs then standard process model metrics for instance fitness and precision are measured.

They found that HMM can provide a reliable method to evaluate model accuracy in the ex- istence of noise besides other common metrics such as precision, fitness and simplicity, which will be discussed in the following section.

Applying HMMs for sequences clustering has been proposed by Elghazel et al. [83] and Silva [84]. In [83], they proposed a hybrid approach of graph-based clustering and HMMs. In the first step, patients pathways are clustered based on a graph clustering method suggested in [85]. The second step is learning HMM for each cluster.

Although this method could suggested a pathway for new different patient, however, this ap- proach applied on healthcare events during hospital stay only which considers relatively short process. The scalability of this approach has not been tested on complex processes. Besides of the same shortcomings of previous methods which is inability to model the mainstream care process.

In similar work of [84], HMMs performed as a framework to do a general sequences clustering method. The clustering relies on the probability of a sequence that may generate from a con- structed HMM. The probability of generating a sequence is calculated and then the sequence is added to the most similar cluster.

This paper has discussed a theoretical framework for applying HMM in process mining but no experimental results were presented.

On the other hand, Khodabandelou et al.[86] have offered a new application of using HMMs to extract intentional process model from business event log (not healthcare processes) where hid- den states correspond to user behaviour. Several HMMs were trained with different number of hidden states suggested by the stakeholder and the best model was selected using a well-known metric the Bayesian information criterion (BIC) .

Moreover, an extended work of that is a comparison between supervised and unsupervised learning is experimented by Khodabandelou et al. [87] using different event logs. The aim was to test if HMM capable to drive new insights on customer strategies comparing with strategies that already known to the stakeholder. They have developed a framework called ‘map miner’ which uses a HMM to learn transitions between customer behaviour and events. Then the transition matrix and observation matrix are imported to a map miner algorithm in order to visualize customers behaviour.

33 2.7. Machine learning techniques for unstructured process discovery

Interestingly, HMM has revealed many strategies more than the expected ones and the results were promising and have been verified by stakeholder. It should be noted that, this method used business event logs which mostly represent structured processes. Also, selecting the best model relied on the validity of BIC metric.

For prediction purpose, Meier et al. [88] suggested a clinical decision support system using HMMs that help physician explore the best treatment flow for a specific cohort of patients and predict the current phase of oncology treatment. Their method has intended to learn two different HMMs with three and seven hidden states which was recommended by physicians with experience using that data.

Li et al.[89] has implemented HMMs for similar goal which is detecting variations in multi-stage treatment disorder. Two steps are included, first, the model identifies treatment stage based on patients data then displays number of variations of the current stage. HMM was learned with annotated processes where stage label is known. Therefore, the model represented high performance in detecting accurate treatment stage.

The following table provides a summary of how HMMs are used in process mining research that have been proposed, the case studies, whether these techniques are available and ready to use and the general approach of adopting HMM. Four out of nine of the proposed meth- ods are applied on healthcare data. Interestingly, the majority of these papers have trained HMMs closely with domain experts or by using a priori clustering technique to divide the pro- cess before process model discovery, which consequently prevents an ideal representation of mainstream process model.

Table 2.2: HMMs approaches and ProM.

HMM in Process mining papers

Case study Available to reuse

Approach

Poelmans et al. [80] Breast cancer patients No multiple HMMs for each a priori set number of clusters Peters et al.[79] Synthetic data for busi-

ness process

No multiple HMMs for each a priori set number of clusters Carrera & Jung [81] Synthetic data for busi-

ness process

No single HMM with a priori set number of states

Rozinat et al. [82] Synthetic data Yes mapping Petri net to HMM Elghazel et al. [83] Real healthcare process No multiple HMMs for each a

priori set number of clusters Silva[84] Synthetic data No theoretical discussion of us- ing HMM for sequence clus- tering

Khodabandelou et al. [87] [86]

Real Eclipse developers log

Intended to install on ProM

single HMM selected by BIC

Meier et al. [88] oncology No two different HMMs where number of states are recom- manded by physicians Li et al. [89] congestive heart failure No single HMM with a priori set

number of states