Three Narratives of Sequence Analysis

How do we relate the distance between two sequences, as given by an algorithm such as optimal matching, to sociologically meaningful notions of similarity and dissimilarity? This has been controversial in sequence analysis. Attention must be paid to how the algorithm operates, and to what sort of distances it generates in empirical practice. We can think of algorithms as giving distinct “narratives” of similarity, derived either formally or heuristically from their operation. This paper compares such narratives for several measures, including the optimal matching algorithm, a duration-weighted combinatorial subsequence algorithm and a time-warping algorithm. The algorithms have different ways of identifying similarity and of accounting for similarity displaced in time. Optimal matching has a narrative of string-editing and alignment, and is best adapted for discrete-time sequences; combinatorial methods focus on common order and produce radically different dissimilarities, differentiating strongly between simple and complex sequences, and treat time as sequential but not scaled; the time-warping algorithm has a narrative of locally warping the time axis, and while it is structurally similar to OM, it can be thought of as more suited to processes in continuous time. Moreover, because the time-warping parameters can be varied over a wide range, it provides a bridge between algorithms like OM, for which time is a (flexible) scale, and combinatorial subsequence algorithms for which time is scale-less order. With this and its continuous-time foundation, time-warping offers a real alternative to OM for lifecourse sequences.