Comparing finite sequences of discrete events with non-uniform time intervals

Abstract Algorithms that quantify the similarity between two sequences of data date back to the mid 20th century. Sequence comparison continues to be active area of research in mathematics, statistics, and computer science, with applications to a wide number of fields including, biology, marketing, and linguistics. While many methods exist for comparing sequences of discrete events, this paper presents a novel method to compare such sequences while also utilizing information available from non-uniform time intervals between events. The Sequence Alignment with Non-Uniform Time Intervals (SAWNUTI) method, an extension of the Smith-Waterman and Needleman-Wunch algorithms, is described and evaluated using a simulation study and two real-world medical data sets (diabetes and eye tracking). Results illustrate the necessity of this method when time is important to consider in the comparison of sequences.