Linear Dynamics: Clustering without identification
This addresses the challenge of clustering multi-dimensional time series with temporal offsets and varying lengths for applications like ECG analysis, though it is incremental as it builds on existing linear dynamical system models.
The paper tackled the problem of clustering time series from linear dynamical systems without full system identification, by developing an algorithm to estimate the eigenvalues of the state-transition matrix, resulting in improved clustering quality on synthetic and ECG data.
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.