Measuring the quality of a clustering algorithm has shown to be as important as the algorithm itself. It is a crucial part of choosing the clustering algorithm that performs best for an input data. Streaming input data have many features that make them much more challenging than static ones. They are endless, varying and emerging with high speeds. This raised new challenges for the clustering algorithms as well as for their evaluation measures. Up till now, external evaluation measures were exclusively used for validating stream clustering algorithms. While external validation requires a ground truth which is not provided in most applications, particularly in the streaming case, internal clustering validation is efficient and realistic. In this article, we analyze the properties and performances of eleven internal clustering measures. In particular, we apply these measures to carefully synthesized stream scenarios to reveal how they react to clusterings on evolving data streams using both k-means-based and density-based clustering algorithms. A series of experimental results show that different from the case with static data, the Calinski-Harabasz index performs the best in coping with common aspects and errors of stream clustering for k-means-based algorithms, while the revised validity index performs the best for density-based ones.

Companies often specify the intended behaviour of their business processes in a process model. Conformance checking techniques allow us to assess to what degree such process models and corresponding process execution data correspond to one another. In recent years, alignments have proven extremely useful for calculating conformance checking statistics. Existing techniques to compute alignments have been developed to be used in an offline, a posteriori setting. However, we are often interested in observing deviations at the moment they occur, rather than days, weeks or even months later. Hence, we need techniques that enable us to perform conformance checking in an online setting. In this paper, we present a novel approach to incrementally compute prefix-alignments, paving the way for real-time online conformance checking. Our experiments show that the reuse of previously computed prefix-alignments enhances memory efficiency, whilst preserving prefix-alignment optimality. Moreover, we show that, in case of computing approximate prefix-alignments, there is a clear trade-off between memory efficiency and approximation error.

Customer journey analysis is a hot topic in marketing. Understanding how the customers behave is crucial and is considered as one of the key drivers of business success. To the best of our knowledge, a data-driven approach to analyze the customer journey is still missing. For instance, web analytics tools like Google Analytics provide an oversimplified version of the user behavior, focusing more on the frequency of page visits rather than discovering the process of the visit itself. On the other hand, customer journey maps have shown their usefulness, but they need to be created manually by domain experts. This paper contributes a novel approach for applying process mining techniques to web log customer journey analysis. Through process mining we are able to (i) discover the process that better describes the user behavior, (ii) find useful insights, (iii) compare the processes of different clusters of users, and then (iv) use this analysis to improve the journey by optimizing some KPIs (Key Performance Indicators) via personalized recommendations based on the user behavior. We show through a real-life case study a proof of the correctness of the introduced concept by improving the recommender accuracy when incorporating additional context information about the journey as extracted from the process model.