Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform

• URL: http://arxiv.org/abs/2512.10191v1
• Date: Thu, 11 Dec 2025 01:04:27 GMT
• Title: Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform
• Authors: Hao Shu, Jicheng Li, Yu Jin, Ling Zhou,
• Abstract summary: Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series.<n>We propose a temporal isometric delay-embedding transform, which constructs a Hankel tensor whose low-rankness is naturally induced by the smoothness and periodicity of the underlying time series.<n>Our proposed model achieves exact recovery, as confirmed by simulation experiments under various non-random missing patterns.
• Score: 6.015902220215394
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series, fundamentally threatening the reliability of data-driven analysis and decision-making. Pure low-rank tensor completion, as a classical data recovery method, falls short in handling non-random missingness, both methodologically and theoretically. Hankel-structured tensor completion models provide a feasible approach for recovering multidimensional time series with non-random missing patterns. However, most Hankel-based multidimensional data recovery methods both suffer from unclear sources of Hankel tensor low-rankness and lack an exact recovery theory for non-random missing data. To address these issues, we propose the temporal isometric delay-embedding transform, which constructs a Hankel tensor whose low-rankness is naturally induced by the smoothness and periodicity of the underlying time series. Leveraging this property, we develop the \textit{Low-Rank Tensor Completion with Temporal Isometric Delay-embedding Transform} (LRTC-TIDT) model, which characterizes the low-rank structure under the \textit{Tensor Singular Value Decomposition} (t-SVD) framework. Once the prescribed non-random sampling conditions and mild incoherence assumptions are satisfied, the proposed LRTC-TIDT model achieves exact recovery, as confirmed by simulation experiments under various non-random missing patterns. Furthermore, LRTC-TIDT consistently outperforms existing tensor-based methods across multiple real-world tasks, including network flow reconstruction, urban traffic estimation, and temperature field prediction. Our implementation is publicly available at https://github.com/HaoShu2000/LRTC-TIDT.

Related papers

• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion [11.949952079083026]
  We propose a novel model, underlineFourier underlineLow-rank and underlineSparse underlineTensor (FLoST)<n>FLoST decomposes the tensor along the temporal dimension using a transform.<n>It captures low-frequency components with low-rank and high-frequency fluctuations with sparsity, resulting in a hybrid structure that efficiently models both smooth and localized variations.
  arXiv  Detail & Related papers  (2025-05-16T13:54:07Z)
• Functional Complexity-adaptive Temporal Tensor Decomposition [21.446684930040266]
  We propose functional underlineComplexity-underlineAdaptive underlineTemporal underlineTensor dunderlineEcomposition (textscCatte)<n>Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors.<n>We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization.
  arXiv  Detail & Related papers  (2025-02-10T05:27:11Z)
• DispFormer: A Pretrained Transformer Incorporating Physical Constraints for Dispersion Curve Inversion [56.64622091009756]
  This study introduces DispFormer, a transformer-based neural network for $v_s$ profile inversion from Rayleigh-wave phase and group dispersion curves.<n>DispFormer processes dispersion data independently at each period, allowing it to handle varying lengths without requiring network modifications or strict alignment between training and testing datasets.
  arXiv  Detail & Related papers  (2025-01-08T09:08:24Z)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values [67.76168547245237]
  We introduce a novel framework called GST-Pro, which utilizes a graphtemporal process and anomaly scorer to detect anomalies. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-01-11T10:10:16Z)
• Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns [77.34726150561087]
  We introduce four complicated missing patterns, including missing and three fiber-like missing cases according to the mode-drivenn fibers. Despite nonity of the objective function in our model, we derive the optimal solutions by integrating alternating data-mputation method of multipliers.
  arXiv  Detail & Related papers  (2022-05-19T08:37:56Z)
• Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover [87.28082715343896]
  We consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. We design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems.
  arXiv  Detail & Related papers  (2021-10-20T06:15:45Z)
• 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)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)

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.