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Knowl. Discov. Data"],"published-print":{"date-parts":[[2025,1,31]]},"abstract":"<jats:p>Tensor decompositions have been successfully applied to multidimensional data recovery. However, classical tensor decompositions are not suitable for emerging spatio-irregular multidimensional data (i.e., spatio-irregular tensor), whose spatial domain is non-rectangular, e.g., spatial transcriptomics data from bioinformatics and semantic units from computer vision. By using preprocessing (e.g., zero-padding or element-wise 0-1 weighting), the spatio-irregular tensor can be converted to a spatio-regular tensor and then classical tensor decompositions can be applied, but this strategy inevitably introduces bias information, leading to artifacts. How to design a tensor-based method suitable for emerging spatio-irregular tensors is an imperative challenge. To address this challenge, we propose a learnable transform-assisted tensor singular value decomposition (LTA-TSVD) for spatio-irregular tensor recovery, which allows us to leverage the intrinsic structure behind the spatio-irregular tensor. Specifically, we design a learnable transform to project the original spatio-irregular tensor into its latent spatio-regular tensor, and then the latent low-rank structure is captured by classical TSVD on the resulting regular tensor. Empowered by LTA-TSVD, we develop spatio-irregular low-rank tensor completion (SIR-LRTC) and spatio-irregular tensor robust principal component analysis (SIR-TRPCA) models for the spatio-irregular tensor imputation and denoising respectively, and we design corresponding solving algorithms with theoretical convergence. Extensive experiments including the spatial transcriptomics data imputation and hyperspectral image denoising show SIR-LRTC and SIR-TRPCA are superior performance to competing approaches and benefit downstream applications.<\/jats:p>","DOI":"10.1145\/3701235","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T14:50:07Z","timestamp":1729522207000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Learnable Transform-Assisted Tensor Decomposition for Spatio-Irregular Multidimensional Data Recovery"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4786-555X","authenticated-orcid":false,"given":"Hao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7766-230X","authenticated-orcid":false,"given":"Ting-Zhu","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6540-946X","authenticated-orcid":false,"given":"Xi-Le","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8223-844X","authenticated-orcid":false,"given":"Shuqin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3866-3737","authenticated-orcid":false,"given":"Jin-Yu","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9099-4154","authenticated-orcid":false,"given":"Tai-Xiang","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6833-5227","authenticated-orcid":false,"given":"Michael K.","family":"Ng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hong Kong Baptist University, Hong Kong, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,12,11]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1145\/3368555.3384464","volume-title":"Proc. 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