Linear Dynamics: Clustering without identification

Chloe Hsu, Michaela Hardt, Moritz Hardt
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:918-929, 2020.

Abstract

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without full system identification. We analyze a computationally efficient and provably convergent algorithm to estimate the eigenvalues of the state-transition matrix in a linear dynamical system.When applied to time series clustering, our algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths, under the assumption that the time series are generated from linear dynamical systems. Evaluating our algorithm on both synthetic data and real electrocardiogram (ECG) signals, we see improvements in clustering quality over existing baselines.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-hsu20b, title = {Linear Dynamics: Clustering without identification}, author = {Hsu, Chloe and Hardt, Michaela and Hardt, Moritz}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {918--929}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/hsu20b/hsu20b.pdf}, url = { http://proceedings.mlr.press/v108/hsu20b.html }, abstract = {Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without full system identification. We analyze a computationally efficient and provably convergent algorithm to estimate the eigenvalues of the state-transition matrix in a linear dynamical system.When applied to time series clustering, our algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths, under the assumption that the time series are generated from linear dynamical systems. Evaluating our algorithm on both synthetic data and real electrocardiogram (ECG) signals, we see improvements in clustering quality over existing baselines.} }
Endnote
%0 Conference Paper %T Linear Dynamics: Clustering without identification %A Chloe Hsu %A Michaela Hardt %A Moritz Hardt %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-hsu20b %I PMLR %P 918--929 %U http://proceedings.mlr.press/v108/hsu20b.html %V 108 %X Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without full system identification. We analyze a computationally efficient and provably convergent algorithm to estimate the eigenvalues of the state-transition matrix in a linear dynamical system.When applied to time series clustering, our algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths, under the assumption that the time series are generated from linear dynamical systems. Evaluating our algorithm on both synthetic data and real electrocardiogram (ECG) signals, we see improvements in clustering quality over existing baselines.
APA
Hsu, C., Hardt, M. & Hardt, M.. (2020). Linear Dynamics: Clustering without identification. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:918-929 Available from http://proceedings.mlr.press/v108/hsu20b.html .

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