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Some mathematical notes on three-mode factor analysis

Citations

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Cited by:

  1. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
  2. Piotr Tarka, 2018. "An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 313-354, January.
  3. Paulo Reis Mourao, 2008. "Towards a Puviani’s Fiscal Illusion Index," Hacienda Pública Española / Review of Public Economics, IEF, vol. 187(4), pages 49-86, December.
  4. Carolyn Anderson, 1996. "The analysis of three-way contingency tables by three-mode association models," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 465-483, September.
  5. Verniest, Fabien & Greulich, Sabine, 2019. "Methods for assessing the effects of environmental parameters on biological communities in long-term ecological studies - A literature review," Ecological Modelling, Elsevier, vol. 414(C).
  6. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
  7. Zhenghao Zeng & Yuqi Gu & Gongjun Xu, 2023. "A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 580-612, June.
  8. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
  9. Werner Kunz, 2007. "Visualization of competitive market structure by means of choice data," Computational Statistics, Springer, vol. 22(4), pages 521-531, December.
  10. Maolin Che & Juefei Chen & Yimin Wei, 2022. "Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 852-877, September.
  11. Violetta Simonacci & Michele Gallo, 2019. "Detecting Public Social Spending Patterns in Italy Using a Three-Way Relative Variation Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 205-219, November.
  12. Domino, Krzysztof, 2020. "Multivariate cumulants in outlier detection for financial data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
  13. 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.
  14. 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.
  15. Cristina Tortora & Mireille Gettler Summa & Marina Marino & Francesco Palumbo, 2016. "Factor probabilistic distance clustering (FPDC): a new clustering method," 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. 10(4), pages 441-464, December.
  16. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
  17. 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.
  18. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
  19. Dawn Iacobucci & Doug Grisaffe, 2018. "Perceptual maps via enhanced correspondence analysis: representing confidence regions to clarify brand positions," Journal of Marketing Analytics, Palgrave Macmillan, vol. 6(3), pages 72-83, September.
  20. 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.
  21. Zhang, Tonglin, 2020. "CP decomposition and weighted clique problem," Statistics & Probability Letters, Elsevier, vol. 161(C).
  22. Ikemoto, Hiroki & Adachi, Kohei, 2016. "Sparse Tucker2 analysis of three-way data subject to a constrained number of zero elements in a core array," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 1-18.
  23. Lombardo, Rosaria & Camminatiello, Ida & D'Ambra, Antonello & Beh, Eric J., 2021. "Assessing the Italian tax courts system by weighted three-way log-ratio analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
  24. Geetanjali Rathee & Hemraj Saini & Sahil Garg & Bong Jun Choi & Mohammad Mehedi Hassan, 2024. "A Secure Data E-Governance for Healthcare Application in Cyber Physical Systems," International Journal on Semantic Web and Information Systems (IJSWIS), IGI Global, vol. 20(1), pages 1-18, January.
  25. 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.
  26. 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.
  27. Nathaniel Helwig, 2013. "The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 725-739, October.
  28. Pan, Chenjian & Ling, Chen & He, Hongjin & Qi, Liqun & Xu, Yanwei, 2024. "A low-rank and sparse enhanced Tucker decomposition approach for tensor completion," Applied Mathematics and Computation, Elsevier, vol. 465(C).
  29. Markus Schröder & Fabien Gatti & David Lauvergnat & Hans-Dieter Meyer & Oriol Vendrell, 2022. "The coupling of the hydrated proton to its first solvation shell," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
  30. Maria Silvana Salvini & Giuseppe Gabrielli & Anna Paterno & Isabella Corazziari, 2015. "Demographic Trends in Developing Countries: Convergence or Divergence Processes?," Econometrics Working Papers Archive 2015_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  31. Víctor Amor-Esteban & Mª-Purificación Galindo-Villardón & Fátima David, 2018. "Study of the Importance of National Identity in the Development of Corporate Social Responsibility Practices: A Multivariate Vision," Administrative Sciences, MDPI, vol. 8(3), pages 1-33, August.
  32. Yunxia Xu & Linzhang Lu & Qilong Liu & Zhen Chen, 2023. "Hypergraph-Regularized L p Smooth Nonnegative Matrix Factorization for Data Representation," Mathematics, MDPI, vol. 11(13), pages 1-27, June.
  33. 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.
  34. Roberto Rocci & Jos Berge, 2002. "Transforming three-way arrays to maximal simplicity," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 351-365, September.
  35. 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.
  36. repec:hum:wpaper:sfb649dp2007-032 is not listed on IDEAS
  37. Bruno Scalzo Dees, 2019. "Analysing Global Fixed Income Markets with Tensors," Papers 1908.02101, arXiv.org, revised Dec 2019.
  38. Roberto Dell'Anno & Adalgiso Amendola, 2015. "Social Exclusion and Economic Growth: An Empirical Investigation in European Economies," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(2), pages 274-301, June.
  39. 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.
  40. 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.
  41. Gower, John, 2016. "Biometrics and Psychometrics: Origins, Commonalities and Differences," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i05).
  42. 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.
  43. D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A least squares approach to Principal Component Analysis for interval valued data," Economics & Statistics Discussion Papers esdp03013, University of Molise, Department of Economics.
  44. Richard Sands & Forrest Young, 1980. "Component models for three-way data: An alternating least squares algorithm with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 39-67, March.
  45. 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.
  46. Søren Kjærgaard & Yunus Emre Ergemen & Marie-Pier Bergeron Boucher & Jim Oeppen & Malene Kallestrup-Lamb, 2019. "Longevity forecasting by socio-economic groups using compositional data analysis," CREATES Research Papers 2019-08, Department of Economics and Business Economics, Aarhus University.
  47. Ballester-Ripoll, Rafael & Paredes, Enrique G. & Pajarola, Renato, 2019. "Sobol tensor trains for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 311-322.
  48. Rosaria Lombardo & Eric J. Beh & Francesco Prattichizzo & Giuseppe Lucisano & Antonio Nicolucci & Björn Eliasson & Hanne Krage Carlsen & Rosalba La Grotta & Valeria Pellegrini & Antonio Ceriello, 2024. "Testing and Visualization of Associations in Three-Way Contingency Tables: A Study of the Gender Gap in Patients with Type 1 Diabetes and Cardiovascular Complications," Mathematics, MDPI, vol. 12(14), pages 1-13, July.
  49. 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.
  50. 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.
  51. 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.
  52. Zhiyuan Zhang & Chen Ling & Hongjin He & Liqun Qi, 2024. "A tensor train approach for internet traffic data completion," Annals of Operations Research, Springer, vol. 339(3), pages 1461-1479, August.
  53. Siciliano, Roberta & Mooijaart, Ab, 1997. "Three-factor association models for three-way contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 337-356, May.
  54. Meyners, Michael & Qannari, El Mostafa, 2001. "Relating principal component analysis on merged data sets to a regression approach," Technical Reports 2001,47, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  55. Andersson, Claus A. & Henrion, Rene, 1999. "A general algorithm for obtaining simple structure of core arrays in N-way PCA with application to fluorometric data," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 255-278, September.
  56. Rodrigo Gutiérrez-Cuevas & Dorian Bouchet & Julien Rosny & Sébastien M. Popoff, 2024. "Reaching the precision limit with tensor-based wavefront shaping," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
  57. Lin Zhu & Junjie Zhang & Scott W. Cunningham, 2022. "Domain expertise extraction for finding rising stars," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(9), pages 5475-5495, September.
  58. Quan Yu & Xinzhen Zhang, 2023. "T-product factorization based method for matrix and tensor completion problems," Computational Optimization and Applications, Springer, vol. 84(3), pages 761-788, April.
  59. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised Jul 2024.
  60. 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.
  61. Laura Anderlucci & Alessandro Lubisco & Stefania Mignani, 2021. "Investigating the Judges Performance in a National Competition of Sport Dance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 783-799, August.
  62. 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.
  63. 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.
  64. Eric Jondeau & Emmanuel Jurczenko & Michael Rockinger, 2018. "Moment Component Analysis: An Illustration With International Stock Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 576-598, October.
  65. Rosaria Lombardo & Eric J. Beh & Luis Guerrero, 2019. "Analysis of three-way non-symmetrical association of food concepts in cross-cultural marketing," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2323-2337, September.
  66. Xinhai Liu & Wolfgang Glänzel & Bart De Moor, 2011. "Hybrid clustering of multi-view data via Tucker-2 model and its application," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(3), pages 819-839, September.
  67. Andrii Babii & Eric Ghysels & Junsu Pan, 2022. "Tensor Principal Component Analysis," Papers 2212.12981, arXiv.org, revised Aug 2023.
  68. Susana Mendes & M. José Fernández-Gómez & Sónia Cotrim Marques & Miguel Ângelo Pardal & Ulisses Miranda Azeiteiro & M. Purificación Galindo-Villardón, 2017. "CO-tucker: a new method for the simultaneous analysis of a sequence of paired tables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2729-2755, November.
  69. DELL'ANNO, Roberto & VILLA, Stefania, 2012. "Growth in Transition Countries: Big Bang versus Gradualism," CELPE Discussion Papers 122, CELPE - CEnter for Labor and Political Economics, University of Salerno, Italy.
  70. 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.
  71. Matheus Pereira Libório & Oseias da Silva Martinuci & Alexei Manso Correa Machado & Renata de Mello Lyrio & Patrícia Bernardes, 2022. "Time–Space Analysis of Multidimensional Phenomena: A Composite Indicator of Social Exclusion Through k-Means," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 159(2), pages 569-591, January.
  72. Serrano Cinca, C. & Mar Molinero, C. & Gallizo Larraz, J.L., 2005. "Country and size effects in financial ratios: A European perspective," Global Finance Journal, Elsevier, vol. 16(1), pages 26-47, August.
  73. Giuseppe Giordano & Steven Haberman & Maria Russolillo, 2019. "Coherent modeling of mortality patterns for age-specific subgroups," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 189-204, June.
  74. Henk Kiers, 1991. "Hierarchical relations among three-way methods," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 449-470, September.
  75. Laurent Sorber & Ignat Domanov & Marc Barel & Lieven Lathauwer, 2016. "Exact line and plane search for tensor optimization," Computational Optimization and Applications, Springer, vol. 63(1), pages 121-142, January.
  76. 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.
  77. Lang Huyan & Ying Li & Dongmei Jiang & Yanning Zhang & Quan Zhou & Bo Li & Jiayuan Wei & Juanni Liu & Yi Zhang & Peng Wang & Hai Fang, 2023. "Remote Sensing Imagery Object Detection Model Compression via Tucker Decomposition," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
  78. Shi, Chengchun & Lu, Wenbin & Song, Rui, 2019. "Determining the number of latent factors in statistical multi-relational learning," LSE Research Online Documents on Economics 102110, London School of Economics and Political Science, LSE Library.
  79. 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.
  80. 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.
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  84. Lin, Jie & Huang, Ting-Zhu & Zhao, Xi-Le & Ma, Tian-Hui & Jiang, Tai-Xiang & Zheng, Yu-Bang, 2021. "A novel non-convex low-rank tensor approximation model for hyperspectral image restoration," Applied Mathematics and Computation, Elsevier, vol. 408(C).
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  88. Quan Yu & Xinzhen Zhang & Zheng-Hai Huang, 2023. "Tensor Factorization-Based Method for Tensor Completion with Spatio-temporal Characterization," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 337-362, October.
  89. 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.
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  94. 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.
  95. 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.
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  97. Pieter Kroonenberg & Jan Leeuw, 1980. "Principal component analysis of three-mode data by means of alternating least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 69-97, March.
  98. Chen Ling & Gaohang Yu & Liqun Qi & Yanwei Xu, 2021. "T-product factorization method for internet traffic data completion with spatio-temporal regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 883-913, December.
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  110. Roberto Dell'Anno & Stefania Villa, 2013. "Growth in transition countries," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 21(3), pages 381-417, July.
  111. Minghui Ding & Yimin Wei & Pengpeng Xie, 2023. "A Randomized Singular Value Decomposition for Third-Order Oriented Tensors," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 358-382, April.
  112. Giordani, Paolo, 2010. "Three-way analysis of imprecise data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 568-582, March.
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  114. Xing, Jiping & Wu, Wei & Cheng, Qixiu & Liu, Ronghui, 2022. "Traffic state estimation of urban road networks by multi-source data fusion: Review and new insights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
  115. Henk Kiers, 1997. "Three-mode orthomax rotation," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 579-598, December.
  116. Giudici, Paolo & Huang, Bihong & Spelta, Alessandro, 2019. "Trade networks and economic fluctuations in Asian countries," Economic Systems, Elsevier, vol. 43(2), pages 1-1.
  117. Raymond Sin-Kwok Wong, 2001. "Multidimensional Association Models," Sociological Methods & Research, , vol. 30(2), pages 197-240, November.
  118. 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.
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