  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}}.
