Time Series Learning using Monotonic Logical Properties

TL;DR

This paper introduces a logic-based framework for analyzing time-series data from cyber-physical systems by embedding domain knowledge into parametric formulas, enabling effective classification and logical specification extraction.

Contribution

It proposes a novel method to map time-series data into a parameter space using logical formulas, facilitating domain-informed distance metrics and data classification.

Findings

Successfully applied to traffic data for classifying slow-downs and jams

Enables domain-specific knowledge embedding into data analysis

Extracts logical specifications from labeled data

Abstract

Cyber-physical systems of today are generating large volumes of time-series data. As manual inspection of such data is not tractable, the need for learning methods to help discover logical structure in the data has increased. We propose a logic-based framework that allows domain-specific knowledge to be embedded into formulas in a parametric logical specification over time-series data. The key idea is to then map a time series to a surface in the parameter space of the formula. Given this mapping, we identify the Hausdorff distance between boundaries as a natural distance metric between two time-series data under the lens of the parametric specification. This enables embedding non-trivial domain-specific knowledge into the distance metric and then using off-the-shelf machine learning tools to label the data. After labeling the data, we demonstrate how to extract a logical specification for each label. Finally, we showcase our technique on real world traffic data to learn classifiers/monitors for slow-downs and traffic jams.