  The ubiquity of sequences in many domains enhances significant recent
interest in sequence learning, for which a basic problem is how to measure the
distance between sequences. Dynamic time warping (DTW) aligns two sequences by
nonlinear local warping and returns a distance value. DTW shows superior
ability in many applications, e.g. video, image, etc. However, in DTW, two
points are paired essentially based on point-to-point Euclidean distance (ED)
without considering the autocorrelation of sequences. Thus, points with
different semantic meanings, e.g. peaks and valleys, may be matched providing
their coordinate values are similar. As a result, DTW is sensitive to noise and
poorly interpretable. This paper proposes an efficient and flexible sequence
alignment algorithm, dynamic state warping (DSW). DSW converts each time point
into a latent state, which endows point-wise autocorrelation information.
Alignment is performed by using the state sequences. Thus DSW is able to yield
alignment that is semantically more interpretable than that of DTW. Using one
nearest neighbor classifier, DSW shows significant improvement on
classification accuracy in comparison to ED (70/85 wins) and DTW (74/85 wins).
We also empirically demonstrate that DSW is more robust and scales better to
long sequences than ED and DTW.
