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Principal component analysis of three-mode data by means of alternating least squares algorithms

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Cited by:

  1. Karel Hron & Paula Brito & Peter Filzmoser, 2017. "Exploratory data analysis for interval compositional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 223-241, June.
  2. Michel Velden & Tammo Bijmolt, 2006. "Generalized canonical correlation analysis of matrices with missing rows: a simulation study," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 323-331, June.
  3. Timmerman, Marieke E. & Kiers, Henk A. L., 2002. "Three-way component analysis with smoothness constraints," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 447-470, September.
  4. Stephan Stahlschmidt & Wolfgang K. H�rdle & Helmut Thome, 2015. "An Application of Principal Component Analysis on Multivariate Time-stationary Spatio-temporal Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(2), pages 160-180, June.
  5. Henk Kiers, 1989. "An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 515-521, September.
  6. Werner Kunz, 2007. "Visualization of competitive market structure by means of choice data," Computational Statistics, Springer, vol. 22(4), pages 521-531, December.
  7. Rubinstein, Alexander & Slutskin, Lev, 2018. "«Multiway data analysis» and the general problem of journals’ ranking," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 50, pages 90-113.
  8. repec:jss:jstsof:34:i10 is not listed on IDEAS
  9. Henk Kiers, 1991. "Hierarchical relations among three-way methods," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 449-470, September.
  10. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
  11. Shenglong Hu, 2020. "An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors," Computational Optimization and Applications, Springer, vol. 75(3), pages 701-737, April.
  12. Richard Harshman & Margaret Lundy, 1996. "Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/candecomp," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 133-154, March.
  13. Kenta Mitsushita & Shin Murakoshi & Masato Koyama, 2023. "How are various natural disasters cognitively represented?: a psychometric study of natural disaster risk perception applying three-mode principal component analysis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 116(1), pages 977-1000, March.
  14. Jos Berge & Jan Leeuw & Pieter Kroonenberg, 1987. "Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 52(2), pages 183-191, June.
  15. Kiers, Henk A. L., 1998. "Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure," Computational Statistics & Data Analysis, Elsevier, vol. 28(3), pages 307-324, September.
  16. Giuseppe Brandi & Ruggero Gramatica & Tiziana Di Matteo, 2019. "Unveil stock correlation via a new tensor-based decomposition method," Papers 1911.06126, arXiv.org, revised Apr 2020.
  17. Caterina Liberati & Paolo Mariani, 2012. "Banking customer satisfaction evaluation: a three-way factor perspective," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(4), pages 323-336, December.
  18. Henk Kiers, 1990. "Majorization as a tool for optimizing a class of matrix functions," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 417-428, September.
  19. Wilderjans, Tom & Ceulemans, Eva & Van Mechelen, Iven, 2009. "Simultaneous analysis of coupled data blocks differing in size: A comparison of two weighting schemes," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1086-1098, February.
  20. Henk Kiers & Pieter Kroonenberg & Jos Berge, 1992. "An efficient algorithm for TUCKALS3 on data with large numbers of observation units," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 415-422, September.
  21. Pieters, Rik G. M. & de Klerk-Warmerdam, Marianne, 1996. "Ad-evoked feelings: Structure and impact on Aad and recall," Journal of Business Research, Elsevier, vol. 37(2), pages 105-114, October.
  22. Veldscholte, Carla M. & Kroonenberg, Pieter M. & Antonides, Gerrit, 1998. "Three-mode analysis of perceptions of economic activities in Eastern and Western Europe1," Journal of Economic Psychology, Elsevier, vol. 19(3), pages 321-351, June.
  23. Paolo Giordani & Roberto Rocci & Giuseppe Bove, 2020. "Factor Uniqueness of the Structural Parafac Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 555-574, September.
  24. Alwin Stegeman, 2018. "Simultaneous Component Analysis by Means of Tucker3," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 21-47, March.
  25. Dahl, Tobias & Naes, Tormod, 2006. "A bridge between Tucker-1 and Carroll's generalized canonical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3086-3098, July.
  26. Alwin Stegeman & Tam Lam, 2014. "Three-Mode Factor Analysis by Means of Candecomp/Parafac," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 426-443, July.
  27. Michael Siegrist & Carmen Keller & Henk A. L. Kiers, 2005. "A New Look at the Psychometric Paradigm of Perception of Hazards," Risk Analysis, John Wiley & Sons, vol. 25(1), pages 211-222, February.
  28. Willem Kloot & Pieter Kroonenberg, 1985. "External analysis with three-mode principal component models," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 479-494, December.
  29. Stegeman, Alwin, 2014. "Finding the limit of diverging components in three-way Candecomp/Parafac—A demonstration of its practical merits," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 203-216.
  30. Kohei Adachi, 2011. "Three-Way Tucker2 Component Analysis Solutions of Stimuli × Responses × Individuals Data with Simple Structure and the Fewest Core Differences," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 285-305, April.
  31. Roberto Rocci & Jos Berge, 2002. "Transforming three-way arrays to maximal simplicity," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 351-365, September.
  32. Schepers, Jan & van Mechelen, Iven & Ceulemans, Eva, 2006. "Three-mode partitioning," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1623-1642, December.
  33. Dawn Iacobucci & Doug Grisaffe & Wayne DeSarbo, 2017. "Statistical perceptual maps: using confidence region ellipses to enhance the interpretations of brand positions in multidimensional scaling," Journal of Marketing Analytics, Palgrave Macmillan, vol. 5(3), pages 81-98, December.
  34. Ji Yeh Choi & Heungsun Hwang & Marieke E. Timmerman, 2018. "Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 1-20, March.
  35. repec:hum:wpaper:sfb649dp2007-032 is not listed on IDEAS
  36. Schoonees, P.C. & Groenen, P.J.F. & van de Velden, M., 2015. "Least-squares Bilinear Clustering of Three-way Data," Econometric Institute Research Papers EI2014-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  37. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
  38. Pieter C. Schoonees & Patrick J. F. Groenen & Michel Velden, 2022. "Least-squares bilinear clustering of three-way data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 1001-1037, December.
  39. Mitzi Cubilla-Montilla & Ana Belén Nieto-Librero & M. Purificación Galindo-Villardón & Carlos A. Torres-Cubilla, 2021. "Sparse HJ Biplot: A New Methodology via Elastic Net," Mathematics, MDPI, vol. 9(11), pages 1-15, June.
  40. Gower, John, 2016. "Biometrics and Psychometrics: Origins, Commonalities and Differences," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i05).
  41. Hildebrandt, Lutz & Klapper, Daniel, 1997. "Möglichkeiten und Ansätze der Analyse dreimodaler Daten für die Marktforschung," SFB 373 Discussion Papers 1997,90, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  42. Mohamed Ibrahim Assoweh & Stéphane Chrétien & Brahim Tamadazte, 2020. "Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation," Mathematics, MDPI, vol. 8(4), pages 1-31, April.
  43. Klapper, Daniel & Cooper, Lee G. & Hildebrandt, Lutz, 1999. "The congruence of theoretical and empirical patterns of inter-store price competition," SFB 373 Discussion Papers 1999,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  44. Henk Kiers, 1997. "Three-mode orthomax rotation," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 579-598, December.
  45. Henk Kiers, 1995. "Maximization of sums of quotients of quadratic forms and some generalizations," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 221-245, June.
  46. Roberto Rocci & Maurizio Vichi, 2005. "Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 715-736, December.
  47. Eva Ceulemans & Iven Mechelen & Iwin Leenen, 2003. "Tucker3 hierarchical classes analysis," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 413-433, September.
  48. Bilian Chen & Zhening Li & Shuzhong Zhang, 2015. "On optimal low rank Tucker approximation for tensors: the case for an adjustable core size," Journal of Global Optimization, Springer, vol. 62(4), pages 811-832, August.
  49. Arie Kapteyn & Heinz Neudecker & Tom Wansbeek, 1986. "An approach ton-mode components analysis," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 269-275, June.
  50. repec:hum:wpaper:sfb649dp2014-016 is not listed on IDEAS
  51. Pieter M. Kroonenberg & Cornelis J. Lammers & Ineke Stoop, 1985. "Three-Mode Principal Component Analysis of Multivariate Longitudinal Organizational Data," Sociological Methods & Research, , vol. 14(2), pages 99-136, November.
  52. Takashi Murakami & Jos Berge & Henk Kiers, 1998. "A case of extreme simplicity of the core matrix in three-mode principal components analysis," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 255-261, September.
  53. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
  54. Carlos Martin-Barreiro & John A. Ramirez-Figueroa & Ana B. Nieto-Librero & Víctor Leiva & Ana Martin-Casado & M. Purificación Galindo-Villardón, 2021. "A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model," Mathematics, MDPI, vol. 9(3), pages 1-22, January.
  55. Piet Brouwer & Pieter Kroonenberg, 1991. "Some notes on the diagonalization of the extended three-mode core matrix," Journal of Classification, Springer;The Classification Society, vol. 8(1), pages 93-98, January.
  56. Giuseppe Brandi & T. Di Matteo, 2020. "A new multilayer network construction via Tensor learning," Papers 2004.05367, arXiv.org.
  57. Elisa Frutos-Bernal & Ángel Martín del Rey & Irene Mariñas-Collado & María Teresa Santos-Martín, 2022. "An Analysis of Travel Patterns in Barcelona Metro Using Tucker3 Decomposition," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
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