  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.
