Specifying and detecting temporal patterns with shape expressions

Modern cyber-physical systems (CPS) and the Internet of things (IoT) are data factories generating, measuring and recording huge amounts of time series. The useful information in time series is usually present in the form of sequential patterns. We propose shape expressions as a declarative language for specification and extraction of rich temporal patterns from possibly noisy data. Shape expressions are regular expressions with arbitrary (linear, exponential, sinusoidal, etc.) shapes with parameters as atomic predicates and additional constraints on these parameters. We associate with shape expressions novel noisy semantics that combines regular expression matching semantics with statistical regression. We study essential properties of the language and propose an efficient heuristic for approximate matching of shape expressions. We demonstrate the applicability of this technique on two case studies from the health and the avionics domains.