# Interpretable Classification of Time-Series Data using Efficient Enumerative Techniques

## TL;DR

This paper introduces an efficient, systematic method for automatically learning interpretable temporal logic formulas from time-series data, enabling better classification and clustering in cyber-physical systems.

## Contribution

It presents a novel approach to explore the entire space of STL formulas without predefined templates, improving interpretability and applicability in real-world domains.

## Key findings

- Successfully applied to automotive, transportation, and healthcare data
- Outperforms existing methods in interpretability and classification accuracy
- Heuristically prunes the formula space to improve efficiency

## Abstract

Cyber-physical system applications such as autonomous vehicles, wearable devices, and avionic systems generate a large volume of time-series data. Designers often look for tools to help classify and categorize the data. Traditional machine learning techniques for time-series data offer several solutions to solve these problems; however, the artifacts trained by these algorithms often lack interpretability. On the other hand, temporal logics, such as Signal Temporal Logic (STL) have been successfully used in the formal methods community as specifications of time-series behaviors. In this work, we propose a new technique to automatically learn temporal logic formulae that are able to cluster and classify real-valued time-series data. Previous work on learning STL formulas from data either assumes a formula-template to be given by the user, or assumes some special fragment of STL that enables exploring the formula structure in a systematic fashion. In our technique, we relax these assumptions, and provide a way to systematically explore the space of all STL formulas. As the space of all STL formulas is very large, and contains many semantically equivalent formulas, we suggest a technique to heuristically prune the space of formulas considered. Finally, we illustrate our technique on various case studies from the automotive, transportation and healthcare domain.