size is determined based on domain knowledge of the data set. In supervised event abstraction we aim for a generic method that works for all XES event logs in general. A time window based approach contrasts with our aim for generality, as no single time window size will be appropriate for all event logs. Furthermore, the durations of the events within a single event log might differ drastically (e.g. one event might take seconds, while another event takes months), in which case time window based approaches will either miss short events in case of larger time windows or resort to very large numbers of time windows resulting in very long computational time. Therefore, we map each individual low-level event to a high-level event and do not use time windows. In a smart home environment context with passive sensors, each change in a binary sensor value can be considered to be a low-level event.

Preliminaries {#sec:preliminaries}
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In this section we introduce basic concepts used throughout the paper.

We use the usual sequence definition, and denote a sequence by listing its elements, e.g. we write $\langle a_1,a_2,\dots,a_{n} \rangle$ for a (finite) sequence $s:\{1,\dots,n\}\to S$ of elements from some alphabet $S$, where 