Interpretable classification of time-series data using efficient enumerative techniques

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.

An automated system repair framework with signal temporal logic

“…Due to its expressivity and efficient algorithms for checking continuous signals against STL formulae, it is used in different areas including monitoring [10,11], fault detection via falsification [18] and formal control [33]. Synthe-sizing an STL formula from a dataset is studied in the literature in different forms such as finding a formula that is satisfied by all system traces to identify the system requirements [24,25], finding a formula that differentiates the given sets of good and bad signals [31], signal clustering [36] or finding a formula that would identify the bad events as they occur [10,17]. The proposed formula synthesis method as a part of the repair framework extends [17] by performing parameter synthesis in each iteration and eliminating formulae that cannot be part of the result for efficiency.…”

Formel Yaklaşımlar ile Sürüm Değerlendirme

“…Formül sentezi problemi, verilen sinyal kümesini en iyi tanımlayacak zamansal mantık formülünün türetilmesi olarak tanımlanır. Bu problem, kullanılan zamansal mantık (STL veya ptSTL), veri kümesinin yapısı, parametrik formüllerin problem girdisi olup olmaması açısından farklı biçimlerde çalışılmıştır (Aydin & Aydin Gol, 2020;Bartocci et al, 2014;Bombara et al, 2016;Ergurtuna & Aydin Gol, 2019;Hoxha et al, 2018;Jha et al, 2019;Jin et al, 2015;Ketenci & Aydin Gol, 2019;Kong et al, 2014;Mohammadinejad et al, 2020;Yoo & Belta, 2017).…”

“…Sistem izlerinden (zaman serisi verisi), bu izleri tanımlayacak STL formüllerinin üretilmesi üzerinde yakın zamanda birçok çalışma yapılmıştır (Aydin & Aydin Gol, 2020;Bartocci, Bortolussi & Sanguinetti, 2014;Bombara, Vasile, Penedo, Yasuoka & Belta, 2016;Ergurtuna & Aydin Gol, 2019;Hoxha, Dokhanchi & Fainekos, 2018;Jha, Tiwari, Seshia, Sahai & Shankar, 2019;Jin, Donzé, Deshmukh & Seshia, 2015;Ketenci & Aydin Gol, 2019;Kong, Jones, Ayala, Aydin Gol & Belta, 2014;Mohammadinejad, Deshmukh, Puranic, Vazquez-Chanlatte & Donzé, 2020;Yoo & Belta, 2017). Bu çalışmalar, veri kümesinin yapısı ve üretilen formül açısından farklılık göstermektedir.…”

“…Bu konudaki bazı çalışmalarda, formül yapısı kullanıcı tarafından belirlenmiş ve belirlenen formül yapısı için parametre bulunmuştur (Hoxha et al, 2017;Jin et al, 2015). İyi ve kötü olarak etiketlenmiş sistem izlerinden, bu izleri doğru şekilde sınıflandırabilecek bir formül bulunması hem gerçek zamanlı sistem izleme hem de sınıflandırıcı üretmek uygulamaları için çalışılmıştır (Aydin & Aydin Gol, 2020;Bartocci et al, 2014;Bombara et al, 2016;Ergurtuna & Aydin Gol, 2019;Ketenci & Aydin Gol, 2019;Kong et al 2014;Mohammadinejad et al, 2020;Yoo & Belta, 2017).…”

Learning Specifications for Labelled Patterns

“…Clustering was used to generate labelling and then construct specifications from monotonic PSTL templates. In [24], monotonic PSTL formulae are enumerated using formula signatures. Computation of validity domain boundaries [22] is combined with checks for misclassification rate for parameter estimation.…”