Time Series Learning using Monotonic Logical Properties

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.

[1]  Calin Belta,et al.  Temporal logic inference for classification and prediction from data , 2014, HSCC.

[2]  Eamonn J. Keogh,et al.  Scaling up dynamic time warping for datamining applications , 2000, KDD '00.

[3]  Dejan Nickovic,et al.  Monitoring Temporal Properties of Continuous Signals , 2004, FORMATS/FTRTFT.

[4]  Yan Liu,et al.  An Examination of Multivariate Time Series Hashing with Applications to Health Care , 2014, 2014 IEEE International Conference on Data Mining.

[5]  Eamonn J. Keogh,et al.  Logical-shapelets: an expressive primitive for time series classification , 2011, KDD.

[6]  Dejan Nickovic,et al.  Parametric Identification of Temporal Properties , 2011, RV.

[7]  Eamonn J. Keogh,et al.  Time series shapelets: a new primitive for data mining , 2009, KDD.

[8]  Garvit Juniwal,et al.  CPSGrader: Synthesizing temporal logic testers for auto-grading an embedded systems laboratory , 2014, 2014 International Conference on Embedded Software (EMSOFT).

[9]  Sanjit A. Seshia,et al.  Mining Requirements From Closed-Loop Control Models , 2015, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[10]  Yan Liu,et al.  Functional Subspace Clustering with Application to Time Series , 2015, ICML.

[11]  Calin Belta,et al.  A Decision Tree Approach to Data Classification using Signal Temporal Logic , 2016, HSCC.

[12]  Ezio Bartocci,et al.  Data-Driven Statistical Learning of Temporal Logic Properties , 2014, FORMATS.

[13]  Sanjit A. Seshia,et al.  Logical Clustering and Learning for Time-Series Data , 2016, CAV.

[14]  Yan Liu,et al.  Sparse-GEV: Sparse Latent Space Model for Multivariate Extreme Value Time Serie Modeling , 2012, ICML.

[15]  Mohan M. Trivedi,et al.  Driver Behavior and Situation Aware Brake Assistance for Intelligent Vehicles , 2007, Proceedings of the IEEE.

[16]  Sanjit A. Seshia,et al.  ST-Lib: A Library for Specifying and Classifying Model Behaviors , 2016, SAE Technical Paper Series.

[17]  Oded Maler.  Learning Monotone Partitions of Partially-Ordered Domains (Work in Progress) , 2017 .

[18]  Jason Lines,et al.  A shapelet transform for time series classification , 2012, KDD.

[19]  Allan Hanbury,et al.  An Efficient Algorithm for Calculating the Exact Hausdorff Distance , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Calin Belta,et al.  Robust Satisfaction of Temporal Logic Specifications via Reinforcement Learning , 2015, ArXiv.

[21]  Calin Belta,et al.  Anomaly detection in cyber-physical systems: A formal methods approach , 2014, 53rd IEEE Conference on Decision and Control.

[22]  Ugur Demiryurek,et al.  Latent Space Model for Road Networks to Predict Time-Varying Traffic , 2016, KDD.

[23]  T. Warren Liao,et al.  Clustering of time series data - a survey , 2005, Pattern Recognit..

[24]  Sanjit A. Seshia,et al.  Logic-based Clustering and Learning for Time-Series Data , 2016 .