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

2025-02-10

AI Summary

Time series exhibit nonlinear temporal misalignments, hindering accurate alignment and averaging—key bottlenecks for conventional analysis methods. To address this, we propose the Diffeomorphic Temporal Alignment Network (DTAN), a framework enabling unsupervised or weakly supervised joint alignment and averaging of variable-length time series collections. Our contributions are threefold: (1) We introduce Inverse-Consistent Averaging Error (ICAE) regularization—a novel, registration-free constraint ensuring diffeomorphic consistency without explicit correspondence supervision; (2) We design Multi-Task DTAN (MT-DTAN), unifying alignment and classification in an end-to-end trainable architecture; (3) We extend Principal Component Analysis (PCA) to unaligned time series for the first time. DTAN leverages input-dependent diffeomorphic deformation prediction, warp regularization, and UCR-compatible backbone designs. Evaluated on all 128 UCR time series classification benchmarks, DTAN consistently outperforms state-of-the-art alignment and averaging methods, achieving significant gains in alignment accuracy and downstream task performance.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• Addressing nonlinear temporal misalignment in time-series
• Joint alignment and averaging of time-series ensembles
• Enabling PCA for misaligned time-series data

Innovation

• Diffeomorphic transformations for alignment
• Inverse Consistency Averaging Error
• Multi-task learning integration