The Shocklet Transform: A Decomposition Method for the Identification of Local, Mechanism-Driven Dynamics in Sociotechnical Time Series

by David Rushing Dewhurst, Thayer Alshaabi, Dilan Kiley, Michael V. Arnold, Joshua R. Minot, Christopher M. Danforth and Peter Sheridan Dodds

https://arxiv.org/pdf/1906.11710.pdf

Abstract: We introduce a qualitative, shape-based, timescale-independent time-domain transform used to extract local dynamics from sociotechnical time series—termed the Discrete Shocklet Transform(DST)—and an associated similarity search routine, the Shocklet Transform And Ranking (STAR)algorithm, that indicates time windows during which panels of time series display qualitatively-similar anomalous behavior. After distinguishing our algorithms from other methods used in anomaly detection and time series similarity search, such as the matrix profile, seasonal-hybrid ESD, and discrete wavelet transform-based procedures, we demonstrate the DSTs ability to identify mechanism-driven dynamics at a wide range of timescales and its relative insensitivity to functional parameterization. As an application, we analyze a sociotechnical data source (usage frequencies fora subset of words on Twitter) and highlight our algorithms utility by using them to extract both a typology of mechanistic local dynamics and a data-driven narrative of socially-important events as perceived by English-language Twitter.