Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignment

TL;DR

This paper introduces a novel diffeomorphic temporal transformer network called ResNet-TW that uses residual networks to generate smooth, invertible time warping functions for aligning time-series data efficiently and accurately.

Contribution

It proposes a new ResNet-based approach inspired by LDDMM for diffeomorphic time-series alignment, enabling smooth and invertible transformations with a single forward pass.

Findings

Achieves competitive alignment and classification performance on diverse datasets.

Generates smooth, invertible warping functions efficiently.

Outperforms or matches existing methods in accuracy and speed.

Abstract

Non-linear (large) time warping is a challenging source of nuisance in time-series analysis. In this paper, we propose a novel diffeomorphic temporal transformer network for both pairwise and joint time-series alignment. Our ResNet-TW (Deep Residual Network for Time Warping) tackles the alignment problem by compositing a flow of incremental diffeomorphic mappings. Governed by the flow equation, our Residual Network (ResNet) builds smooth, fluid and regular flows of velocity fields and consequently generates smooth and invertible transformations (i.e. diffeomorphic warping functions). Inspired by the elegant Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, the final transformation is built by the flow of time-dependent vector fields which are none other than the building blocks of our Residual Network. The latter is naturally viewed as an Eulerian discretization schema of the flow equation (an ODE). Once trained, our ResNet-TW aligns unseen data by a single inexpensive forward pass. As we show in experiments on both univariate (84 datasets from UCR archive) and multivariate time-series (MSR Action-3D, Florence-3D and MSR Daily Activity), ResNet-TW achieves competitive performance in joint alignment and classification.