{"ID":2830044,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10191","arxiv_id":"2512.10191","title":"Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform","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.","short_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 methodologicall...","url_abs":"https://arxiv.org/abs/2512.10191","url_pdf":"https://arxiv.org/pdf/2512.10191v1","authors":"[\"Hao Shu\",\"Jicheng Li\",\"Yu Jin\",\"Ling Zhou\"]","published":"2025-12-11T01:04:27Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":605992,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2830044,"paper_url":"https://arxiv.org/abs/2512.10191","paper_title":"Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform","repo_url":"https://github.com/HaoShu2000/LRTC-TIDT","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}