  Many real-world applications require aligning two temporal sequences,
including bioinformatics, handwriting recognition, activity recognition, and
human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment
method, but can fail on high-dimensional real-world data where the dimensions
of aligned sequences are often unequal. In this paper, we show that exploiting
the multiscale manifold latent structure of real-world data can yield improved
alignment. We introduce a novel framework called Warping on Wavelets (WOW) that
integrates DTW with a a multi-scale manifold learning framework called
Diffusion Wavelets. We present a theoretical analysis of the WOW family of
algorithms and show that it outperforms previous state of the art methods, such
as canonical time warping (CTW) and manifold warping, on several real-world
datasets.
