Multiscale Manifold Warping

TL;DR

This paper introduces Warping on Wavelets (WOW), a novel multiscale manifold learning framework that enhances temporal sequence alignment by integrating Diffusion Wavelets with Dynamic Time Warping, outperforming existing methods.

Contribution

The paper presents a new multiscale manifold warping framework called WOW that combines DTW with Diffusion Wavelets for improved alignment of high-dimensional sequences.

Findings

WOW outperforms CTW and manifold warping on real datasets.

Theoretical analysis supports the effectiveness of WOW.

Multiscale manifold structure improves alignment accuracy.

Abstract

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.