Random Warping Series: A Random Features Method for Time-Series Embedding
This work addresses computational bottlenecks in time-series classification and clustering for researchers and practitioners, offering a more scalable alternative to existing DTW-based methods, though it is incremental as it builds on prior kernel and random features techniques.
The authors tackled the computational inefficiency and diagonal dominance issues of Dynamic Time Warping (DTW)-based kernels for time-series analysis by proposing Random Warping Series (RWS), a kernel with a random features approximation that reduces complexity from quadratic to linear in sample size and length, and demonstrated its effectiveness by outperforming or matching state-of-the-art methods on 16 benchmark datasets in accuracy and computational time.
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels have since been proposed in the spirit of DTW to extend its use to kernel-based estimation method such as support vector machine. However, those kernels suffer from diagonal dominance of the Gram matrix and a quadratic complexity w.r.t. the sample size. In this work, we study a family of alignment-aware positive definite (p.d.) kernels, with its feature embedding given by a distribution of \emph{Random Warping Series (RWS)}. The proposed kernel does not suffer from the issue of diagonal dominance while naturally enjoys a \emph{Random Features} (RF) approximation, which reduces the computational complexity of existing DTW-based techniques from quadratic to linear in terms of both the number and the length of time-series. We also study the convergence of the RF approximation for the domain of time series of unbounded length. Our extensive experiments on 16 benchmark datasets demonstrate that RWS outperforms or matches state-of-the-art classification and clustering methods in both accuracy and computational time. Our code and data is available at { \url{https://github.com/IBM/RandomWarpingSeries}}.