Linear Dynamics: Clustering without identification

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 b...

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Bibliographic Details
Published in:arXiv.org 2020-02
Main Authors: Hsu, Chloe Ching-Yun, Hardt, Michaela, Hardt, Moritz
Format: Article
Language:English
Subjects:
Algorithms
Clustering
Dynamical systems
Electrocardiography
Mathematical models
Multidimensional data
Offsets
Parameter identification
Sequences
Time series
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Summary: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.
ISSN:2331-8422