Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging

TL;DR

This paper introduces an advanced diffeomorphic neural network framework for unsupervised time-series alignment and averaging, addressing nonlinear misalignment challenges with novel regularization strategies and multi-task learning, validated on extensive datasets.

Contribution

The paper presents the DTAN framework with a novel ICAE regularization-free method, extends it to multi-task learning, and evaluates various architectures, advancing time-series joint alignment and averaging techniques.

Findings

Outperforms existing averaging methods on 128 UCR datasets

Demonstrates effectiveness of ICAE in variable-length signal alignment

Shows benefits of multi-task learning in time-series analysis

Abstract

In time-series analysis, nonlinear temporal misalignment remains a pivotal challenge that forestalls even simple averaging. Since its introduction, the Diffeomorphic Temporal Alignment Net (DTAN), which we first introduced (Weber et al., 2019) and further developed in (Weber & Freifeld, 2023), has proven itself as an effective solution for this problem (these conference papers are earlier partial versions of the current manuscript). DTAN predicts and applies diffeomorphic transformations in an input-dependent manner, thus facilitating the joint alignment (JA) and averaging of time-series ensembles in an unsupervised or a weakly-supervised manner. The inherent challenges of the weakly/unsupervised setting, particularly the risk of trivial solutions through excessive signal distortion, are mitigated using either one of two distinct strategies: 1) a regularization term for warps; 2) using the Inverse Consistency Averaging Error (ICAE). The latter is a novel, regularization-free approach which also facilitates the JA of variable-length signals. We also further extend our framework to incorporate multi-task learning (MT-DTAN), enabling simultaneous time-series alignment and classification. Additionally, we conduct a comprehensive evaluation of different backbone architectures, demonstrating their efficacy in time-series alignment tasks. Finally, we showcase the utility of our approach in enabling Principal Component Analysis (PCA) for misaligned time-series data. Extensive experiments across 128 UCR datasets validate the superiority of our approach over contemporary averaging methods, including both traditional and learning-based approaches, marking a significant advancement in the field of time-series analysis.