# Mining Interpretable Spatio-temporal Logic Properties for Spatially Distributed Systems

arXiv: https://arxiv.org/abs/2106.08548 · HTML: https://mlsanity.com/paper/2106.08548/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 7 of 7)

- [Interpretable Classification of Time-Series Data using Efficient Enumerative Techniques](https://mlsanity.com/paper/1907.10265/) (2019)
- [Monitoring Mobile and Spatially Distributed Cyber-Physical Systems](https://mlsanity.com/paper/1904.08847/) (2019)
- [Logic-based Clustering and Learning for Time-Series Data](https://mlsanity.com/paper/1612.07823/) (2016)
- [Qualitative and Quantitative Monitoring of Spatio-Temporal Properties with SSTL](https://mlsanity.com/paper/1706.09334/) (2017)
- [Mining Environment Assumptions for Cyber-Physical System Models](https://mlsanity.com/paper/2005.08435/) (2020)
- [Time Series Learning using Monotonic Logical Properties](https://mlsanity.com/paper/1802.08924/) (2018)
- [MoonLight: A Lightweight Tool for Monitoring Spatio-Temporal Properties](https://mlsanity.com/paper/2104.14333/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Spatio-Temporal Specifications for Dynamical Systems](https://mlsanity.com/paper/2112.10714/) (2021)

## Abstract (arXiv)

The Internet-of-Things, complex sensor networks, multi-agent cyber-physical systems are all examples of spatially distributed systems that continuously evolve in time. Such systems generate huge amounts of spatio-temporal data, and system designers are often interested in analyzing and discovering structure within the data. There has been considerable interest in learning causal and logical properties of temporal data using logics such as Signal Temporal Logic (STL); however, there is limited work on discovering such relations on spatio-temporal data. We propose the first set of algorithms for unsupervised learning for spatio-temporal data. Our method does automatic feature extraction from the spatio-temporal data by projecting it onto the parameter space of a parametric spatio-temporal reach and escape logic (PSTREL). We propose an agglomerative hierarchical clustering technique that guarantees that each cluster satisfies a distinct STREL formula. We show that our method generates STREL formulas of bounded description complexity using a novel decision-tree approach which generalizes previous unsupervised learning techniques for Signal Temporal Logic. We demonstrate the effectiveness of our approach on case studies from diverse domains such as urban transportation, epidemiology, green infrastructure, and air quality monitoring.