Mining Shape Expressions from Positive Examples

Abstract

Shape expressions (SEs) is a novel specification language that was recently introduced to express behavioral patterns over real-valued signals observed during the execution of cyber-physical systems. An SE is a regular expression composed of arbitrary parameterized shapes, such as lines, exponential curves, and sinusoids as atomic symbols with symbolic constraints on the shape parameters. SEs enable a natural and intuitive specification of complex temporal patterns over possibly noisy data. In this article, we propose a novel method for mining a broad and interesting fragment of SEs from time-series data using a combination of techniques from linear regression, unsupervised clustering, and learning finite automata from positive examples. The learned SE for a given dataset provides an explainable and intuitive model of the observed system behavior. We demonstrate the applicability of our approach on two case studies from different application domains and experimentally evaluate the implemented specification mining procedure.