Logic-based Clustering and Learning for Time-Series Data

TL;DR

This paper introduces a logic-based approach using monotonic PSTL to generate interpretable features for unsupervised clustering of time-series data, aiding analysis of complex cyberphysical systems.

Contribution

It presents a novel method combining PSTL with machine learning for interpretable, unsupervised classification of time-series data in CPS contexts.

Findings

Produces interpretable PSTL formulas for clustering

Applied successfully to automotive, traffic, and online course data

Facilitates understanding of complex time-series patterns

Abstract

To effectively analyze and design cyberphysical systems (CPS), designers today have to combat the data deluge problem, i.e., the burden of processing intractably large amounts of data produced by complex models and experiments. In this work, we utilize monotonic Parametric Signal Temporal Logic (PSTL) to design features for unsupervised classification of time series data. This enables using off-the-shelf machine learning tools to automatically cluster similar traces with respect to a given PSTL formula. We demonstrate how this technique produces interpretable formulas that are amenable to analysis and understanding using a few representative examples. We illustrate this with case studies related to automotive engine testing, highway traffic analysis, and auto-grading massively open online courses.