Time Series Classification through Diffeomorphic Time Warping (DiffTW)

• URL: http://arxiv.org/abs/2606.23472v1
• Date: Mon, 22 Jun 2026 15:18:24 GMT
• Title: Time Series Classification through Diffeomorphic Time Warping (DiffTW)
• Abstract summary: We propose a theoretical framework that learns mappings between real-valued functions.<n>These mappings approximate the flow associated with the characteristic curves of a linear transport equation with a space-dependent velocity field.<n>Our method, Diffeomorphic Time Warping (DiffTW), provides a theoretically grounded dissimilarity measure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time series classification involves learning a mapping from a continuous, temporally ordered sequence of real-valued observations to a discrete response variable, like class labels. This task is fundamental in domains, including health monitoring, where the temporal structure of data is critical for accurate prediction. Dynamic Time Warping (DTW) is a standard technique for measuring similarity between sequences varying in time or speed. However, DTW is restricted to discrete point matching. To move beyond pairwise alignment, we propose a theoretical framework that learns mappings between real-valued functions. These mappings approximate the flow associated with the characteristic curves of a linear transport equation with a space-dependent velocity field, providing a diffeomorphic transformation between two time series. Using the method of characteristics, we transform this partial differential equation into ordinary differential equations (ODEs) modeling system dynamics. The objective function used to learn these ODEs derives from the fundamental theorem of calculus. To enable flexible, expressive representations of the velocity field, we utilize reproducing kernel Hilbert spaces and optimal control methods. Our method, Diffeomorphic Time Warping (DiffTW), provides a theoretically grounded dissimilarity measure. Using a 1-nearest neighbor classifier, DiffTW outperforms DTW on 60 of 86 datasets.

Related papers

• Parallel Complex Diffusion for Scalable Time Series Generation [50.01609741902786]
  PaCoDi is a spectral-native architecture that decouples generative modeling in the frequency domain.<n>We show that PaCoDi outperforms existing baselines in both generation quality and inference speed.
  arXiv  Detail & Related papers  (2026-02-10T14:31:53Z)
• T-Graphormer: Using Transformers for Spatiotemporal Forecasting [2.855856661274715]
  T-Graphormer reduces root mean squared error (RMSE) and mean absolute percentage error (MAPE) by up to 20% and 10%.<n>We show the effectiveness of T-Graphormer on real-world traffic prediction benchmark datasets.
  arXiv  Detail & Related papers  (2025-01-22T23:32:29Z)
• Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping [0.0]
  The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. This thesis proposes novel elastic alignment methods that use parametric & diffeomorphic warping transformations.
  arXiv  Detail & Related papers  (2023-09-25T10:51:47Z)
• OTW: Optimal Transport Warping for Time Series [75.69837166816501]
  Dynamic Time Warping (DTW) has become the pragmatic choice for measuring distance between time series. It suffers from unavoidable quadratic time complexity when the optimal alignment matrix needs to be computed exactly. We introduce a new metric for time series data based on the Optimal Transport framework, called Optimal Transport Warping (OTW)
  arXiv  Detail & Related papers  (2023-06-01T12:45:00Z)
• Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Paths [54.53208538517505]
  This paper addresses learning end-to-end models for time series data that include a temporal alignment step via dynamic time warping (DTW) We propose a DTW layer based around bi-level optimisation and deep declarative networks, which we name DecDTW. We show that this property is particularly useful for applications where downstream loss functions are defined on the optimal alignment path itself.
  arXiv  Detail & Related papers  (2023-03-19T21:58:37Z)
• Approximating DTW with a convolutional neural network on EEG data [9.409281517596396]
  We propose a fast and differentiable approximation of Dynamic Time Wrapping (DTW) We show that our methods achieve at least the same level of accuracy as other DTW main approximations with higher computational efficiency.
  arXiv  Detail & Related papers  (2023-01-30T13:27:47Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition [20.55025648415664]
  We propose NON FActor Trajectory learning for dynamic tensor decomposition (NONFAT) We use a second-level GP to sample the entry values and to capture the temporal relationship between the entities. We have shown the advantage of our method in several real-world applications.
  arXiv  Detail & Related papers  (2022-07-06T05:33:00Z)
• Closed-Form Diffeomorphic Transformations for Time Series Alignment [0.0]
  We present a closed-form expression for the ODE solution and its gradient under continuous piecewise-affine velocity functions. Results show significant improvements both in terms of efficiency and accuracy.
  arXiv  Detail & Related papers  (2022-06-16T12:02:12Z)
• STRODE: Stochastic Boundary Ordinary Differential Equation [30.237665903943963]
  Most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio inputs. We present a probabilistic ordinary differential equation (ODE) that learns both the timings and the dynamics of time series data without requiring any timing annotations during training. Our results show that our approach successfully infers event timings of time series data.
  arXiv  Detail & Related papers  (2021-07-17T16:25:46Z)
• Aligning Time Series on Incomparable Spaces [83.8261699057419]
  We propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces.
  arXiv  Detail & Related papers  (2020-06-22T22:19:28Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.