Explaining Interval Sequences by Randomization

Abstract. Sequences of events are an ubiquitous form of data. In this paper, we show that it is feasible to present an event sequence as an interval sequence. We show how sequences can be efficiently randomized, how to choose a correct null model and how to use randomizations to derive confidence intervals. Using these techniques, we gain knowledge of the temporal structure of the sequence. Time and Fourier space representations, autocorrelations and arbitrary features can be used as constraints in investigating the data. The methods presented are applied to two real-life datasets; a medical heart interbeat interval dataset and a word dataset from a book. We find that the interval sequence representation and randomization methods provide a powerful way to explore interval sequences and explain their structure.