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By itself, it is a non-unique matrix factorization problem, while unique solutions can be obtained by imposing additional assumptions such as statistical independence. By mapping the matrix data to a tensor and by using tensor decompositions afterwards, uniqueness is ensured under certain conditions. Tensor decompositions have been studied thoroughly in literature. We discuss the matrix to tensor step and present tensorization as an important concept on itself, illustrated by a number of stochastic and deterministic tensorization techniques.","is_dataset_classified":null,"base_score":3.4965075614664802,"endowment":3.4965075614664802,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21097893","pmcid":null,"openalex_id":"https://openalex.org/W1538092215","authors":[],"funders":[{"funder_name":"European Commission","grant_id":"339804","title":"Biomedical Data Fusion using Tensor based Blind Source Separation"}],"total_grants":1,"fwci":null,"citation_percentile":null,"influential_citations":0,"citation_trend":[{"year":2015,"count":1},{"year":2016,"count":4},{"year":2017,"count":7},{"year":2018,"count":4},{"year":2019,"count":4},{"year":2020,"count":2},{"year":2021,"count":2},{"year":2022,"count":4},{"year":2023,"count":2},{"year":2024,"count":1},{"year":2025,"count":1}],"oa_status":"green","license":"other-oa","oa_locations":[{"url":"https://lirias.kuleuven.be/handle/123456789/503082","host_type":"repository"},{"url":"https://lirias.kuleuven.be/handle/123456789/503082","host_type":"repository"},{"url":"https://link.springer.com/content/pdf/10.1007/978-3-319-22482-4_1","host_type":"publisher"},{"url":"https://doi.org/10.1007/978-3-319-22482-4_1","host_type":"book series"},{"url":"https://lirias.kuleuven.be/bitstream/123456789/503082/3/15-54.pdf","host_type":""},{"url":"https://dx.doi.org/10.1007/978-3-319-22482-4_1","host_type":""}],"fields_of_study":["Blind Source Separation Techniques","Tensor decomposition and applications","Speech and Audio Processing","02 engineering and technology","0202 electrical engineering, electronic engineering, information engineering"],"mesh_terms":[],"keywords":["Blind signal separation","Tensor (intrinsic definition)","Computer science","Independence (probability theory)","Matrix (chemical analysis)","Mixing (physics)","Algorithm","Uniqueness","Source separation","Matrix decomposition","SIGNAL (programming language)","Factorization","Signal processing","Matrix analysis","Applied mathematics","Mathematics","Pure mathematics","Mathematical analysis","Statistics","Physics","Technology","Science & Technology","Computer Science, Information Systems","CANONICAL POLYADIC DECOMPOSITION","SISTA","COMPONENT ANALYSIS","Higher-order tensor","Independent component analysis","Computer Science, Artificial Intelligence","Tensorization","POLYNOMIALS","Computer Science, Theory & Methods","MATRIX FACTORIZATION","Blind source separation","Block term decomposition","Multilinear algebra"],"sdg_mappings":[{"sdg_number":2,"sdg_label":"2. 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