Size matters: choosing the most informative set of window lengths for mining patterns in event sequences

In order to find patterns in data, it is often necessary to aggregate or summarise data at a higher level of granularity. Selecting the appropriate granularity is a challenging task and often no principled solutions exist. This problem is particularly relevant in analysis of data with sequential structure. We consider this problem for a specific type of data, namely event sequences. We introduce the problem of finding the best set of window lengths for analysis of event sequences for algorithms with real-valued output. We present suitable criteria for choosing one or multiple window lengths and show that these naturally translate into a computational optimisation problem. We show that the problem is NP-hard in general, but that it can be approximated efficiently and even analytically in certain cases. We give examples of tasks that demonstrate the applicability of the problem and present extensive experiments on both synthetic data and real data from several domains. We find that the method works well in practice, and that the optimal sets of window lengths themselves can provide new insight into the data