Spikelet: An Adaptive Symbolic Approximation for Finding Higher-Level Structure in Time Series

Time series motifs have become a fundamental tool to characterize repeated and conserved structures in systems, such as manufacturing, human behavior and economic activities. Recently the notion of semantic motif was introduced as a generalization of motifs that allows the capture of higher-level semantic structure. Sematic motifs are a very promising primitive; however, the original work characterizes a semantic motif with only two sub-patterns separated by a variable length don't-care region, so it may fail to capture certain types of regularities embedded in a time series. To mitigate this weakness, we propose an adaptive, symbolic and spike-based approximation that allows overlapping segmentation, which we call spikelet. The adaptive and overlapping nature of our representation is more expressive, enabling it to capture both global and local characteristics of a conserved structure. Furthermore, the symbolic nature of our proposed representation enables us to reason about the "grammatical" structure of the data. With extensive empirical work, we show that spikelet-based algorithms are scalable enough for real-world datasets and enables us to find the higher-level structure that would otherwise escape our attention.