Tensor rank decomposition (English Wikipedia)
Analysis of information sources in references of the Wikipedia article "Tensor rank decomposition" in English language version.
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ams.org
- Bocci, Cristiano; Chiantini, Luca (2013). "On the identifiability of binary Segre products". Journal of Algebraic Geometry. 22 (1): 1–11. arXiv:1105.3643. doi:10.1090/s1056-3911-2011-00592-4. ISSN 1056-3911. S2CID 119671913.
arxiv.org
- Hillar, C. J.; Lim, L. (2013). "Most tensor problems are NP-Hard". Journal of the ACM. 60 (6): 1–39. arXiv:0911.1393. doi:10.1145/2512329. S2CID 1460452.
- de Silva, V.; Lim, L. (2008). "Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem". SIAM Journal on Matrix Analysis and Applications. 30 (3): 1084–1127. arXiv:math/0607647. doi:10.1137/06066518x. S2CID 7159193.
- Abo, H.; Ottaviani, G.; Peterson, C. (2009). "Induction for secant varieties of Segre varieties". Transactions of the American Mathematical Society. 361 (2): 767–792. arXiv:math/0607191. doi:10.1090/s0002-9947-08-04725-9. S2CID 59069541.
- Blehkerman, G.; Teitler, Z. (2015). "On maximum, typical and generic ranks". Mathematische Annalen. 362 (3–4): 1–11. arXiv:1402.2371. doi:10.1007/s00208-014-1150-3. S2CID 14309435.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2014-01-01). "An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors". SIAM Journal on Matrix Analysis and Applications. 35 (4): 1265–1287. arXiv:1403.4157. doi:10.1137/140961389. ISSN 0895-4798. S2CID 28478606.
- Bocci, Cristiano; Chiantini, Luca; Ottaviani, Giorgio (2014-12-01). "Refined methods for the identifiability of tensors". Annali di Matematica Pura ed Applicata. 193 (6): 1691–1702. arXiv:1303.6915. doi:10.1007/s10231-013-0352-8. ISSN 0373-3114. S2CID 119721371.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2017-01-01). "Effective Criteria for Specific Identifiability of Tensors and Forms". SIAM Journal on Matrix Analysis and Applications. 38 (2): 656–681. arXiv:1609.00123. doi:10.1137/16m1090132. ISSN 0895-4798. S2CID 23983015.
- Chiantini, L.; Ottaviani, G. (2012-01-01). "On Generic Identifiability of 3-Tensors of Small Rank". SIAM Journal on Matrix Analysis and Applications. 33 (3): 1018–1037. arXiv:1103.2696. doi:10.1137/110829180. ISSN 0895-4798. S2CID 43781880.
- Hauenstein, J. D.; Oeding, L.; Ottaviani, G.; Sommese, A. J. (2016). "Homotopy techniques for tensor decomposition and perfect identifiability". J. Reine Angew. Math. 2019 (753): 1–22. arXiv:1501.00090. doi:10.1515/crelle-2016-0067. S2CID 16324593.
- Bocci, Cristiano; Chiantini, Luca (2013). "On the identifiability of binary Segre products". Journal of Algebraic Geometry. 22 (1): 1–11. arXiv:1105.3643. doi:10.1090/s1056-3911-2011-00592-4. ISSN 1056-3911. S2CID 119671913.
- Domanov, Ignat; Lathauwer, Lieven De (January 2014). "Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition". SIAM Journal on Matrix Analysis and Applications. 35 (2): 636–660. arXiv:1312.2848. doi:10.1137/130916084. ISSN 0895-4798. S2CID 14851072.
- Domanov, Ignat; De Lathauwer, Lieven (January 2017). "Canonical polyadic decomposition of third-order tensors: Relaxed uniqueness conditions and algebraic algorithm". Linear Algebra and Its Applications. 513: 342–375. arXiv:1501.07251. doi:10.1016/j.laa.2016.10.019. ISSN 0024-3795. S2CID 119729978.
- Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. (May 2013). "General tensor decomposition, moment matrices and applications". Journal of Symbolic Computation. 52: 51–71. arXiv:1105.1229. doi:10.1016/j.jsc.2012.05.012. ISSN 0747-7171. S2CID 14181289.
- Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard (December 2017). "Tensor decomposition and homotopy continuation". Differential Geometry and Its Applications. 55: 78–105. arXiv:1512.04312. doi:10.1016/j.difgeo.2017.07.009. ISSN 0926-2245. S2CID 119147635.
doi.org
- F. L. Hitchcock (1927). "The expression of a tensor or a polyadic as a sum of products". Journal of Mathematics and Physics. 6 (1–4): 164–189. doi:10.1002/sapm192761164.
- Carroll, J. D.; Chang, J. (1970). "Analysis of individual differences in multidimensional scaling via an n-way generalization of 'Eckart–Young' decomposition". Psychometrika. 35 (3): 283–319. doi:10.1007/BF02310791. S2CID 50364581.
- Hillar, C. J.; Lim, L. (2013). "Most tensor problems are NP-Hard". Journal of the ACM. 60 (6): 1–39. arXiv:0911.1393. doi:10.1145/2512329. S2CID 1460452.
- de Silva, V.; Lim, L. (2008). "Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem". SIAM Journal on Matrix Analysis and Applications. 30 (3): 1084–1127. arXiv:math/0607647. doi:10.1137/06066518x. S2CID 7159193.
- Strassen, V. (1983). "Rank and optimal computation of generic tensors". Linear Algebra and Its Applications. 52/53: 645–685. doi:10.1016/0024-3795(83)80041-x.
- Catalisano, M. V.; Geramita, A. V.; Gimigliano, A. (2002). "Ranks of tensors, secant varieties of Segre varieties and fat points". Linear Algebra and Its Applications. 355 (1–3): 263–285. doi:10.1016/s0024-3795(02)00352-x.
- Abo, H.; Ottaviani, G.; Peterson, C. (2009). "Induction for secant varieties of Segre varieties". Transactions of the American Mathematical Society. 361 (2): 767–792. arXiv:math/0607191. doi:10.1090/s0002-9947-08-04725-9. S2CID 59069541.
- Lickteig, Thomas (1985). "Typical tensorial rank". Linear Algebra and Its Applications. 69: 95–120. doi:10.1016/0024-3795(85)90070-9.
- Catalisano, M. V.; Geramita, A. V.; Gimigliano, A. (2011). "Secant varieties of 1 × ··· × 1 (n-times) are not defective for n ≥ 5". Journal of Algebraic Geometry. 20 (2): 295–327. doi:10.1090/s1056-3911-10-00537-0.
- Blehkerman, G.; Teitler, Z. (2015). "On maximum, typical and generic ranks". Mathematische Annalen. 362 (3–4): 1–11. arXiv:1402.2371. doi:10.1007/s00208-014-1150-3. S2CID 14309435.
- Bini, D.; Lotti, G.; Romani, F. (1980). "Approximate solutions for the bilinear form computational problem". SIAM Journal on Scientific Computing. 9 (4): 692–697. doi:10.1137/0209053.
- Harris, Joe (1992). Algebraic Geometry SpringerLink. Graduate Texts in Mathematics. Vol. 133. doi:10.1007/978-1-4757-2189-8. ISBN 978-1-4419-3099-6.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2014-01-01). "An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors". SIAM Journal on Matrix Analysis and Applications. 35 (4): 1265–1287. arXiv:1403.4157. doi:10.1137/140961389. ISSN 0895-4798. S2CID 28478606.
- Bocci, Cristiano; Chiantini, Luca; Ottaviani, Giorgio (2014-12-01). "Refined methods for the identifiability of tensors". Annali di Matematica Pura ed Applicata. 193 (6): 1691–1702. arXiv:1303.6915. doi:10.1007/s10231-013-0352-8. ISSN 0373-3114. S2CID 119721371.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2017-01-01). "Effective Criteria for Specific Identifiability of Tensors and Forms". SIAM Journal on Matrix Analysis and Applications. 38 (2): 656–681. arXiv:1609.00123. doi:10.1137/16m1090132. ISSN 0895-4798. S2CID 23983015.
- Chiantini, L.; Ottaviani, G. (2012-01-01). "On Generic Identifiability of 3-Tensors of Small Rank". SIAM Journal on Matrix Analysis and Applications. 33 (3): 1018–1037. arXiv:1103.2696. doi:10.1137/110829180. ISSN 0895-4798. S2CID 43781880.
- Hauenstein, J. D.; Oeding, L.; Ottaviani, G.; Sommese, A. J. (2016). "Homotopy techniques for tensor decomposition and perfect identifiability". J. Reine Angew. Math. 2019 (753): 1–22. arXiv:1501.00090. doi:10.1515/crelle-2016-0067. S2CID 16324593.
- Bocci, Cristiano; Chiantini, Luca (2013). "On the identifiability of binary Segre products". Journal of Algebraic Geometry. 22 (1): 1–11. arXiv:1105.3643. doi:10.1090/s1056-3911-2011-00592-4. ISSN 1056-3911. S2CID 119671913.
- Domanov, Ignat; Lathauwer, Lieven De (January 2014). "Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition". SIAM Journal on Matrix Analysis and Applications. 35 (2): 636–660. arXiv:1312.2848. doi:10.1137/130916084. ISSN 0895-4798. S2CID 14851072.
- Domanov, Ignat; De Lathauwer, Lieven (January 2017). "Canonical polyadic decomposition of third-order tensors: Relaxed uniqueness conditions and algebraic algorithm". Linear Algebra and Its Applications. 513: 342–375. arXiv:1501.07251. doi:10.1016/j.laa.2016.10.019. ISSN 0024-3795. S2CID 119729978.
- Faber, Nicolaas (Klaas) M.; Ferré, Joan; Boqué, Ricard (January 2001). "Iteratively reweighted generalized rank annihilation method". Chemometrics and Intelligent Laboratory Systems. 55 (1–2): 67–90. doi:10.1016/s0169-7439(00)00117-9. ISSN 0169-7439.
- Leurgans, S. E.; Ross, R. T.; Abel, R. B. (October 1993). "A Decomposition for Three-Way Arrays". SIAM Journal on Matrix Analysis and Applications. 14 (4): 1064–1083. doi:10.1137/0614071. ISSN 0895-4798.
- Lorber, Avraham. (October 1985). "Features of quantifying chemical composition from two-dimensional data array by the rank annihilation factor analysis method". Analytical Chemistry. 57 (12): 2395–2397. doi:10.1021/ac00289a052. ISSN 0003-2700.
- Sanchez, Eugenio; Kowalski, Bruce R. (January 1990). "Tensorial resolution: A direct trilinear decomposition". Journal of Chemometrics. 4 (1): 29–45. doi:10.1002/cem.1180040105. ISSN 0886-9383. S2CID 120459386.
- Sands, Richard; Young, Forrest W. (March 1980). "Component models for three-way data: An alternating least squares algorithm with optimal scaling features". Psychometrika. 45 (1): 39–67. doi:10.1007/bf02293598. ISSN 0033-3123. S2CID 121003817.
- Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. (May 2013). "General tensor decomposition, moment matrices and applications". Journal of Symbolic Computation. 52: 51–71. arXiv:1105.1229. doi:10.1016/j.jsc.2012.05.012. ISSN 0747-7171. S2CID 14181289.
- Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard (December 2017). "Tensor decomposition and homotopy continuation". Differential Geometry and Its Applications. 55: 78–105. arXiv:1512.04312. doi:10.1016/j.difgeo.2017.07.009. ISSN 0926-2245. S2CID 119147635.
semanticscholar.org
api.semanticscholar.org
- Carroll, J. D.; Chang, J. (1970). "Analysis of individual differences in multidimensional scaling via an n-way generalization of 'Eckart–Young' decomposition". Psychometrika. 35 (3): 283–319. doi:10.1007/BF02310791. S2CID 50364581.
- Hillar, C. J.; Lim, L. (2013). "Most tensor problems are NP-Hard". Journal of the ACM. 60 (6): 1–39. arXiv:0911.1393. doi:10.1145/2512329. S2CID 1460452.
- de Silva, V.; Lim, L. (2008). "Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem". SIAM Journal on Matrix Analysis and Applications. 30 (3): 1084–1127. arXiv:math/0607647. doi:10.1137/06066518x. S2CID 7159193.
- Abo, H.; Ottaviani, G.; Peterson, C. (2009). "Induction for secant varieties of Segre varieties". Transactions of the American Mathematical Society. 361 (2): 767–792. arXiv:math/0607191. doi:10.1090/s0002-9947-08-04725-9. S2CID 59069541.
- Blehkerman, G.; Teitler, Z. (2015). "On maximum, typical and generic ranks". Mathematische Annalen. 362 (3–4): 1–11. arXiv:1402.2371. doi:10.1007/s00208-014-1150-3. S2CID 14309435.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2014-01-01). "An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors". SIAM Journal on Matrix Analysis and Applications. 35 (4): 1265–1287. arXiv:1403.4157. doi:10.1137/140961389. ISSN 0895-4798. S2CID 28478606.
- Bocci, Cristiano; Chiantini, Luca; Ottaviani, Giorgio (2014-12-01). "Refined methods for the identifiability of tensors". Annali di Matematica Pura ed Applicata. 193 (6): 1691–1702. arXiv:1303.6915. doi:10.1007/s10231-013-0352-8. ISSN 0373-3114. S2CID 119721371.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2017-01-01). "Effective Criteria for Specific Identifiability of Tensors and Forms". SIAM Journal on Matrix Analysis and Applications. 38 (2): 656–681. arXiv:1609.00123. doi:10.1137/16m1090132. ISSN 0895-4798. S2CID 23983015.
- Chiantini, L.; Ottaviani, G. (2012-01-01). "On Generic Identifiability of 3-Tensors of Small Rank". SIAM Journal on Matrix Analysis and Applications. 33 (3): 1018–1037. arXiv:1103.2696. doi:10.1137/110829180. ISSN 0895-4798. S2CID 43781880.
- Hauenstein, J. D.; Oeding, L.; Ottaviani, G.; Sommese, A. J. (2016). "Homotopy techniques for tensor decomposition and perfect identifiability". J. Reine Angew. Math. 2019 (753): 1–22. arXiv:1501.00090. doi:10.1515/crelle-2016-0067. S2CID 16324593.
- Bocci, Cristiano; Chiantini, Luca (2013). "On the identifiability of binary Segre products". Journal of Algebraic Geometry. 22 (1): 1–11. arXiv:1105.3643. doi:10.1090/s1056-3911-2011-00592-4. ISSN 1056-3911. S2CID 119671913.
- Domanov, Ignat; Lathauwer, Lieven De (January 2014). "Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition". SIAM Journal on Matrix Analysis and Applications. 35 (2): 636–660. arXiv:1312.2848. doi:10.1137/130916084. ISSN 0895-4798. S2CID 14851072.
- Domanov, Ignat; De Lathauwer, Lieven (January 2017). "Canonical polyadic decomposition of third-order tensors: Relaxed uniqueness conditions and algebraic algorithm". Linear Algebra and Its Applications. 513: 342–375. arXiv:1501.07251. doi:10.1016/j.laa.2016.10.019. ISSN 0024-3795. S2CID 119729978.
- Sanchez, Eugenio; Kowalski, Bruce R. (January 1990). "Tensorial resolution: A direct trilinear decomposition". Journal of Chemometrics. 4 (1): 29–45. doi:10.1002/cem.1180040105. ISSN 0886-9383. S2CID 120459386.
- Sands, Richard; Young, Forrest W. (March 1980). "Component models for three-way data: An alternating least squares algorithm with optimal scaling features". Psychometrika. 45 (1): 39–67. doi:10.1007/bf02293598. ISSN 0033-3123. S2CID 121003817.
- Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. (May 2013). "General tensor decomposition, moment matrices and applications". Journal of Symbolic Computation. 52: 51–71. arXiv:1105.1229. doi:10.1016/j.jsc.2012.05.012. ISSN 0747-7171. S2CID 14181289.
- Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard (December 2017). "Tensor decomposition and homotopy continuation". Differential Geometry and Its Applications. 55: 78–105. arXiv:1512.04312. doi:10.1016/j.difgeo.2017.07.009. ISSN 0926-2245. S2CID 119147635.
ucr.edu
cs.ucr.edu
- Papalexakis, Evangelos. "Automatic Unsupervised Tensor Mining with Quality Assessment" (PDF).
- Gujral, Ekta. "Aptera: Automatic PARAFAC2 Tensor Analysis" (PDF). ASONAM 2022.
uwo.ca
publish.uwo.ca
- Harshman, Richard A. (1970). "Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-modal factor analysis" (PDF). UCLA Working Papers in Phonetics. 16: 84. No. 10,085. Archived from the original (PDF) on October 10, 2004.
web.archive.org
- Harshman, Richard A. (1970). "Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-modal factor analysis" (PDF). UCLA Working Papers in Phonetics. 16: 84. No. 10,085. Archived from the original (PDF) on October 10, 2004.
worldcat.org
search.worldcat.org
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2014-01-01). "An Algorithm For Generic and Low-Rank Specific Identifiability of Complex Tensors". SIAM Journal on Matrix Analysis and Applications. 35 (4): 1265–1287. arXiv:1403.4157. doi:10.1137/140961389. ISSN 0895-4798. S2CID 28478606.
- Bocci, Cristiano; Chiantini, Luca; Ottaviani, Giorgio (2014-12-01). "Refined methods for the identifiability of tensors". Annali di Matematica Pura ed Applicata. 193 (6): 1691–1702. arXiv:1303.6915. doi:10.1007/s10231-013-0352-8. ISSN 0373-3114. S2CID 119721371.
- Chiantini, L.; Ottaviani, G.; Vannieuwenhoven, N. (2017-01-01). "Effective Criteria for Specific Identifiability of Tensors and Forms". SIAM Journal on Matrix Analysis and Applications. 38 (2): 656–681. arXiv:1609.00123. doi:10.1137/16m1090132. ISSN 0895-4798. S2CID 23983015.
- Chiantini, L.; Ottaviani, G. (2012-01-01). "On Generic Identifiability of 3-Tensors of Small Rank". SIAM Journal on Matrix Analysis and Applications. 33 (3): 1018–1037. arXiv:1103.2696. doi:10.1137/110829180. ISSN 0895-4798. S2CID 43781880.
- Bocci, Cristiano; Chiantini, Luca (2013). "On the identifiability of binary Segre products". Journal of Algebraic Geometry. 22 (1): 1–11. arXiv:1105.3643. doi:10.1090/s1056-3911-2011-00592-4. ISSN 1056-3911. S2CID 119671913.
- Domanov, Ignat; Lathauwer, Lieven De (January 2014). "Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition". SIAM Journal on Matrix Analysis and Applications. 35 (2): 636–660. arXiv:1312.2848. doi:10.1137/130916084. ISSN 0895-4798. S2CID 14851072.
- Domanov, Ignat; De Lathauwer, Lieven (January 2017). "Canonical polyadic decomposition of third-order tensors: Relaxed uniqueness conditions and algebraic algorithm". Linear Algebra and Its Applications. 513: 342–375. arXiv:1501.07251. doi:10.1016/j.laa.2016.10.019. ISSN 0024-3795. S2CID 119729978.
- Faber, Nicolaas (Klaas) M.; Ferré, Joan; Boqué, Ricard (January 2001). "Iteratively reweighted generalized rank annihilation method". Chemometrics and Intelligent Laboratory Systems. 55 (1–2): 67–90. doi:10.1016/s0169-7439(00)00117-9. ISSN 0169-7439.
- Leurgans, S. E.; Ross, R. T.; Abel, R. B. (October 1993). "A Decomposition for Three-Way Arrays". SIAM Journal on Matrix Analysis and Applications. 14 (4): 1064–1083. doi:10.1137/0614071. ISSN 0895-4798.
- Lorber, Avraham. (October 1985). "Features of quantifying chemical composition from two-dimensional data array by the rank annihilation factor analysis method". Analytical Chemistry. 57 (12): 2395–2397. doi:10.1021/ac00289a052. ISSN 0003-2700.
- Sanchez, Eugenio; Kowalski, Bruce R. (January 1990). "Tensorial resolution: A direct trilinear decomposition". Journal of Chemometrics. 4 (1): 29–45. doi:10.1002/cem.1180040105. ISSN 0886-9383. S2CID 120459386.
- Sands, Richard; Young, Forrest W. (March 1980). "Component models for three-way data: An alternating least squares algorithm with optimal scaling features". Psychometrika. 45 (1): 39–67. doi:10.1007/bf02293598. ISSN 0033-3123. S2CID 121003817.
- Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. (May 2013). "General tensor decomposition, moment matrices and applications". Journal of Symbolic Computation. 52: 51–71. arXiv:1105.1229. doi:10.1016/j.jsc.2012.05.012. ISSN 0747-7171. S2CID 14181289.
- Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard (December 2017). "Tensor decomposition and homotopy continuation". Differential Geometry and Its Applications. 55: 78–105. arXiv:1512.04312. doi:10.1016/j.difgeo.2017.07.009. ISSN 0926-2245. S2CID 119147635.