Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments

• URL: http://arxiv.org/abs/2203.05813v1
• Date: Fri, 11 Mar 2022 09:46:22 GMT
• Title: Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments
• Authors: Hicham Janati and Marco Cuturi and Alexandre Gramfort
• Abstract summary: We show that our proposed loss can be used to define temporal-temporal baryechecenters as Fr'teche means duality. Experiments on handwritten letters and brain imaging data confirm our theoretical findings.
• Score: 110.79706180350507
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data analysis. We propose in this work a new framework to carry out averaging of these datasets, with the goal of synthesizing a representative template trajectory from multiple trajectories. We show that this requires addressing three sources of invariance: shifts in time, space, and total population size (or mass/amplitude). Here we draw inspiration from dynamic time warping (DTW), optimal transport (OT) theory and its unbalanced extension (UOT) to propose a criterion that can address all three issues. This proposal leverages a smooth formulation of DTW (Soft-DTW) that is shown to capture temporal shifts, and UOT to handle both variations in space and size. Our proposed loss can be used to define spatio-temporal barycenters as Fr\'echet means. Using Fenchel duality, we show how these barycenters can be computed efficiently, in parallel, via a novel variant of entropy-regularized debiased UOT. Experiments on handwritten letters and brain imaging data confirm our theoretical findings and illustrate the effectiveness of the proposed loss for spatio-temporal data.

Related papers

• Cross Space and Time: A Spatio-Temporal Unitized Model for Traffic Flow Forecasting [16.782154479264126]
  Predicting backbone-temporal traffic flow presents challenges due to complex interactions between temporal factors. Existing approaches address these dimensions in isolation, neglecting their critical interdependencies. In this paper, we introduce Sanonymous-Temporal Unitized Unitized Cell (ASTUC), a unified framework designed to capture both spatial and temporal dependencies.
  arXiv  Detail & Related papers  (2024-11-14T07:34:31Z)
• ArrivalNet: Predicting City-wide Bus/Tram Arrival Time with Two-dimensional Temporal Variation Modeling [10.788986436621364]
  This paper proposes textitArrivalNet, a two-dimensional temporal variation-based multi-step ATP for buses and trams. It decomposes the one-dimensional temporal sequence into intra-periodic and inter-periodic variations, which can be recast into two-dimensional tensors. The transformed 2D blocks in different frequencies have an image-like feature representation that enables effective learning with computer vision backbones.
  arXiv  Detail & Related papers  (2024-10-17T10:17:23Z)
• OPUS: Occupancy Prediction Using a Sparse Set [64.60854562502523]
  We present a framework to simultaneously predict occupied locations and classes using a set of learnable queries. OPUS incorporates a suite of non-trivial strategies to enhance model performance. Our lightest model achieves superior RayIoU on the Occ3D-nuScenes dataset at near 2x FPS, while our heaviest model surpasses previous best results by 6.1 RayIoU.
  arXiv  Detail & Related papers  (2024-09-14T07:44:22Z)
• Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks [50.2033914945157]
  We present a representation learning framework, Intensity Profile Projection, for continuous-time dynamic network data. The framework consists of three stages: estimating pairwise intensity functions, learning a projection which minimises a notion of intensity reconstruction error. Moreoever, we develop estimation theory providing tight control on the error of any estimated trajectory, indicating that the representations could even be used in quite noise-sensitive follow-on analyses.
  arXiv  Detail & Related papers  (2023-06-09T15:38:25Z)
• Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction [60.60223171143206]
  Trajectory prediction is a crucial undertaking in understanding entity movement or human behavior from observed sequences. Current methods often assume that the observed sequences are complete while ignoring the potential for missing values. This paper presents a unified framework, the Graph-based Conditional Variational Recurrent Neural Network (GC-VRNN), which can perform trajectory imputation and prediction simultaneously.
  arXiv  Detail & Related papers  (2023-03-28T14:27:27Z)
• Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach [76.45949280328838]
  We propose a Laplacian enhanced low-rank tensor (LETC) framework featuring both lowrankness and multi-temporal correlations for large-scale traffic speed kriging. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging.
  arXiv  Detail & Related papers  (2022-10-21T07:25:57Z)
• Joint Characterization of Spatiotemporal Data Manifolds [0.0]
  Dimensionality reduction (DR) is a type of characterization designed to mitigate the "curse of dimensionality" on high-D signals. Recent years have seen the additional development of a suite of nonlinear DR algorithms, frequently categorized as "manifold learning" Here, we show these three DR approaches can yield complementary information about ST manifold topology.
  arXiv  Detail & Related papers  (2021-08-21T16:42:22Z)
• Low-Rank Hankel Tensor Completion for Traffic Speed Estimation [7.346671461427793]
  We propose a purely data-driven and model-free solution to the traffic state estimation problem. By imposing a low-rank assumption on this tensor structure, we can approximate characterize both global patterns and the unknown complex local dynamics. We conduct numerical experiments on both synthetic simulation data and real-world high-resolution data, and our results demonstrate the effectiveness and superiority of the proposed model.
  arXiv  Detail & Related papers  (2021-05-21T00:08:06Z)
• Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation [4.9831085918734805]
  Missing data imputation has been a long-standing research topic and critical application for real-world intelligent transportation systems. We propose a low-rank autoregressive tensor completion (LATC) framework by introducing textittemporal variation as a new regularization term. We conduct extensive numerical experiments on several real-world traffic data sets, and our results demonstrate the effectiveness of LATC in diverse missing scenarios.
  arXiv  Detail & Related papers  (2021-04-30T12:00:57Z)
• Multi-Temporal Convolutions for Human Action Recognition in Videos [83.43682368129072]
  We present a novel temporal-temporal convolution block that is capable of extracting at multiple resolutions. The proposed blocks are lightweight and can be integrated into any 3D-CNN architecture.
  arXiv  Detail & Related papers  (2020-11-08T10:40:26Z)

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.