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Autor:
Paolo Giordani, Henk A.L. Kiers
Publikováno v:
Statistics in Medicine, 37(1), 137-156. Wiley
In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at different occasions. The occasions can b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::22894ba20341e6e09294ad188fea5855
https://pubmed.ncbi.nlm.nih.gov/29023942
https://pubmed.ncbi.nlm.nih.gov/29023942
Autor:
Alwin Stegeman, Tam T. T. Lam
Publikováno v:
Psychometrika, 79(3), 426-443. SPRINGER
A three-mode covariance matrix contains covariances of N observations (e.g., subject scores) on J variables for K different occasions or conditions. We model such an JK×JK covariance matrix as the sum of a (common) covariance matrix having Candecomp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eea5ec5ac8b851ca7991e07ed2dc0cab
https://research.rug.nl/en/publications/2fd8186c-3209-4b6f-b537-2ffcf98eb443
https://research.rug.nl/en/publications/2fd8186c-3209-4b6f-b537-2ffcf98eb443
Autor:
Tam T. T. Lam, Alwin Stegeman
Publikováno v:
SIAM Journal on Matrix Analysis and Applications, 33(4), 1250-1271
In this paper, we derive improved uniqueness conditions for a constrained version of the canonical order-3 tensor decomposition, also known as Candecomp/Parafac (CP). CP decomposes a three-way array into a prespecified number of outer product arrays.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db7b90cc2de3212f9f59bf356c1d17d1
https://doi.org/10.1137/110847275
https://doi.org/10.1137/110847275
Autor:
Alwin Stegeman
Publikováno v:
Linear Algebra and Its Applications, 431(1-2), 211-227
In the Candecomp/Parafac (CP) model, a three-way array X is written as the sum of R outer vector product arrays and a residual array. The former comprise the columns of the component matrices A , B and C . For fixed residuals, ( A , B , C ) is unique
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6d69672b485670b853df2b3b3e8fa0a
https://doi.org/10.1016/j.laa.2009.02.025
https://doi.org/10.1016/j.laa.2009.02.025
Publikováno v:
Linear Algebra and Its Applications, 430(2-3), 818-829
Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2009, 430 (2-3), pp.818-829. ⟨10.1016/j.laa.2008.09.023⟩
Linear Algebra and its Applications, Elsevier, 2009, 430 (2-3), pp.818-829. 〈10.1016/j.laa.2008.09.023〉
Linear Algebra and its Applications, 2009, 430 (2-3), pp.818-829. ⟨10.1016/j.laa.2008.09.023⟩
Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2009, 430 (2-3), pp.818-829. ⟨10.1016/j.laa.2008.09.023⟩
Linear Algebra and its Applications, Elsevier, 2009, 430 (2-3), pp.818-829. 〈10.1016/j.laa.2008.09.023〉
Linear Algebra and its Applications, 2009, 430 (2-3), pp.818-829. ⟨10.1016/j.laa.2008.09.023⟩
The Candecomp/Parafac algorithm approximates a set of matrices X 1 , … , X I by products of the form AC i B ′ , with C i diagonal, i = 1 , … , I . Carroll and Chang have conjectured that, when the matrices are symmetric, the resulting A and B w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7aaea2c083f560129d2298efb5f0badb
https://doi.org/10.1016/j.laa.2008.09.023
https://doi.org/10.1016/j.laa.2008.09.023
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 30(4):1614-1638
Computing the Candecomp/Parafac (CP) solution of R components (i.e., the best rank-R approximation) for a generic I x J x 2 array may result in diverging components, also known as "degeneracy." In such a case, several components are highly correlated
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dris___00893::c4216056ab34ce63ea8c52f6788dbdc6
https://hdl.handle.net/11370/12e102b0-ba85-4bc7-8fa4-540ab58353e2
https://hdl.handle.net/11370/12e102b0-ba85-4bc7-8fa4-540ab58353e2
Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
Publikováno v:
Psychometrika, 71(2), 219-229. SPRINGER
A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decompose
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::319a51590a25e95b2db666866eaae5fd
https://doi.org/10.1007/11336-006-1278-2
https://doi.org/10.1007/11336-006-1278-2
Autor:
Alwin Stegeman, Jos M. F. ten Berge
Publikováno v:
Computational Statistics and Data Analysis, 50(1), 210-220. ELSEVIER SCIENCE BV
A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. Kruskal has previously shown that the three component matrices involved are essentially unique when the sum of their k-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::385dfbb72bc38b8f34e6f8ad9eaa371a
https://research.rug.nl/en/publications/ec9e0de5-0952-410b-b951-3388044c1577
https://research.rug.nl/en/publications/ec9e0de5-0952-410b-b951-3388044c1577
Autor:
Jos M. F. ten Berge
Publikováno v:
Journal of Chemometrics, 18(1), 12-16
A key property of CANDECOMP/PARAFAC is the essential uniqueness it displays under certain conditions. It has been known for a long time that, when these conditions are not met, partial uniqueness may remain. Whereas considerable progress has been mad
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a6bd5b4eb1610d275b8bbffd88e1939
https://hdl.handle.net/11370/fbc2a57c-bec4-423b-8df4-9cde92a09917
https://hdl.handle.net/11370/fbc2a57c-bec4-423b-8df4-9cde92a09917