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To address this limitation, this letter introduces a tproductinduced Tucker decomposition (tTucker) model that replaces the mode product in Tucker decomposition with t-product, which jointly extends the ideas of t-SVD and high-order SVD. This letter defines the rank of the tTucker decomposition and presents an LRTC model that minimizes the induced Schatten-p norm. An efficient alternating direction multiplier method (ADMM) algorithm is developed to optimize the proposed LRTC model, and its effectiveness is demonstrated through experiments conducted on both synthetic and real data sets, showcasing excellent performance.<\/jats:p>","DOI":"10.1162\/neco_a_01756","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T19:52:00Z","timestamp":1745351520000},"page":"1171-1192","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":0,"title":["Low-Rank, High-Order Tensor Completion via t- Product-Induced Tucker (tTucker) Decomposition"],"prefix":"10.1162","volume":"37","author":[{"given":"Yaodong","family":"Li","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, P.R.C."},{"name":"Key Laboratory of Intelligent Detection and the Internet of Things in Manufacturing, Ministry of Education, 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