A Symbolic Representation of Two -Dimensional Time Series for Arbitrary Length DTW Motif

Over the last two decades, time series motif discovery has emerged as a useful primitive; in parallel, it has been known that Dynamic Time Warping (DTW) outperforms other similarity measures, such as Euclidean Distance, under most settings. In this background, an algorithm for scalable DTW motif discovery was proposed; however, it is limited to one-dimensional (1D) and fixed-length subsequences. In contrast, two-dimensional (2D) DTW presents distinct challenges as it involves warping against the target time series and managing lags between dimensions. We propose a general symbolic representation for 2D time series, enabling the discovery of arbitrary -length motifs with warping and lags. In the motion capture (MoCap) community, a 'text-like representation' for similarity search has been previously proposed. However, it requires multiple parameters and an exhaustive dataset. In contrast, our method relies on just one parameter: the "magnitude threshold," which captures the value fluctuations without requiring an exhaustive dataset. Furthermore, we empirically demonstrate that our method is scalable enough for various real-world datasets and can effectively identify 2D DTW motifs of arbitrary lengths.