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The approximation of one matrix by another of lower rank

Citations

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Cited by:

  1. Yang, Jing-Hua & Zhao, Xi-Le & Ji, Teng-Yu & Ma, Tian-Hui & Huang, Ting-Zhu, 2020. "Low-rank tensor train for tensor robust principal component analysis," Applied Mathematics and Computation, Elsevier, vol. 367(C).
  2. Harold Gulliksen, 1961. "Measurement of learning and mental abilities," Psychometrika, Springer;The Psychometric Society, vol. 26(1), pages 93-107, March.
  3. Peter Schönemann, 1971. "The minimum average correlation between equivalent sets of uncorrelated factors," Psychometrika, Springer;The Psychometric Society, vol. 36(1), pages 21-30, March.
  4. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
  5. Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
  6. Kohei Adachi, 2022. "Factor Analysis Procedures Revisited from the Comprehensive Model with Unique Factors Decomposed into Specific Factors and Errors," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 967-991, September.
  7. Joseph Kruskal & Roger Shepard, 1974. "A nonmetric variety of linear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 39(2), pages 123-157, June.
  8. Jonathan Gillard & Anatoly Zhigljavsky, 2013. "Optimization challenges in the structured low rank approximation problem," Journal of Global Optimization, Springer, vol. 57(3), pages 733-751, November.
  9. Kyusoon Kim & Hee‐Seok Oh & Minsu Park, 2023. "Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
  10. Stanley Mulaik, 1986. "Factor analysis and Psychometrika: Major developments," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 23-33, March.
  11. Cajo Braak, 1990. "Interpreting canonical correlation analysis through biplots of structure correlations and weights," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 519-531, September.
  12. Kohei Adachi & Nickolay T. Trendafilov, 2016. "Sparse principal component analysis subject to prespecified cardinality of loadings," Computational Statistics, Springer, vol. 31(4), pages 1403-1427, December.
  13. Luis Pilacuan-Bonete & Purificación Galindo-Villardón & Francisco Delgado-Álvarez, 2022. "HJ-Biplot as a Tool to Give an Extra Analytical Boost for the Latent Dirichlet Assignment (LDA) Model: With an Application to Digital News Analysis about COVID-19," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
  14. John Ross, 1966. "A remark on tucker and Messick's “points of view” analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 27-31, March.
  15. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 33-42, March.
  16. Charpentier, Arthur & Mussard, Stéphane & Ouraga, Téa, 2021. "Principal component analysis: A generalized Gini approach," European Journal of Operational Research, Elsevier, vol. 294(1), pages 236-249.
  17. 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.
  18. Merola, Giovanni Maria & Chen, Gemai, 2019. "Projection sparse principal component analysis: An efficient least squares method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 366-382.
  19. Tao Pham Dinh & Van Ngai Huynh & Hoai An Le Thi & Vinh Thanh Ho, 2022. "Alternating DC algorithm for partial DC programming problems," Journal of Global Optimization, Springer, vol. 82(4), pages 897-928, April.
  20. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
  21. Jos Berge, 1977. "Orthogonal procrustes rotation for two or more matrices," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 267-276, June.
  22. Paul Horst, 1937. "A method of factor analysis by means of which all coordinates of the factor matrix are given simultaneously," Psychometrika, Springer;The Psychometric Society, vol. 2(4), pages 225-236, December.
  23. Groenen, P.J.F. & van de Velden, M., 2002. "Inverse correspondence analysis," Econometric Institute Research Papers EI 2002-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  24. Torres Lacomba, Anna, 2003. "A comparison between correspondence analysis and categorical conjoint measurement," DEE - Working Papers. Business Economics. WB wb037117, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  25. Terry Gleason & Richard Staelin, 1975. "A proposal for handling missing data," Psychometrika, Springer;The Psychometric Society, vol. 40(2), pages 229-252, June.
  26. Peter Schönemann, 1970. "On metric multidimensional unfolding," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 349-366, September.
  27. Juan Carlos Carrasco Baquero & Verónica Lucía Caballero Serrano & Fernando Romero Cañizares & Daisy Carolina Carrasco López & David Alejandro León Gualán & Rufino Vieira Lanero & Fernando Cobo-Gradín, 2023. "Water Quality Determination Using Soil and Vegetation Communities in the Wetlands of the Andes of Ecuador," Land, MDPI, vol. 12(8), pages 1-18, August.
  28. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.
  29. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
  30. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
  31. Sophie Marque-Pucheu & Guillaume Perrin & Josselin Garnier, 2020. "An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs," Computational Statistics, Springer, vol. 35(3), pages 1059-1099, September.
  32. John C. Gower & Niël J. Le Roux & Sugnet Gardner-Lubbe, 2022. "Properties of individual differences scaling and its interpretation," Statistical Papers, Springer, vol. 63(4), pages 1221-1245, August.
  33. Köhn, Hans-Friedrich, 2010. "Representation of individual differences in rectangular proximity data through anti-Q matrix decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2343-2357, October.
  34. Dray, Stephane, 2008. "On the number of principal components: A test of dimensionality based on measurements of similarity between matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2228-2237, January.
  35. Lejeune, Michel & Calinski, Tadeusz, 2000. "Canonical Analysis Applied to Multivariate Analysis of Variance," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 100-119, January.
  36. Norman Cliff, 1962. "Analytic rotation to a functional relationship," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 283-295, September.
  37. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
  38. Matsuda, Takeru & Strawderman, William E., 2019. "Improved loss estimation for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 300-311.
  39. Richard Johnson, 1966. "The minimal transformation to orthonormality," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 61-66, March.
  40. W. Gibson, 1963. "On the symmetric treatment of an asymmetric approach to factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 28(4), pages 423-426, December.
  41. Alfredo Garcia Hiernaux & Miguel Jerez & José Casals, 2005. "Unit Roots and Cointegrating Matrix Estimation using Subspace Methods," Documentos de Trabajo del ICAE 0512, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  42. Adele Ravagnani & Fabrizio Lillo & Paola Deriu & Piero Mazzarisi & Francesca Medda & Antonio Russo, 2024. "Dimensionality reduction techniques to support insider trading detection," Papers 2403.00707, arXiv.org, revised May 2024.
  43. 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.
  44. Carmen C. Rodríguez-Martínez & Isabel María García-Sánchez & Purificación Vicente-Galindo & Purificación Galindo-Villardón, 2019. "Exploring Relationships between Environmental Performance, E-Government and Corruption: A Multivariate Perspective," Sustainability, MDPI, vol. 11(22), pages 1-16, November.
  45. 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.
  46. Christian Haedo & Michel Mouchart, 2022. "Two-mode clustering through profiles of regions and sectors," Empirical Economics, Springer, vol. 63(4), pages 1971-1996, October.
  47. Robert Lissitz & Peter Schönemann & James Lingoes, 1976. "A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 547-550, December.
  48. Torokhti, Anatoli & Friedland, Shmuel, 2009. "Towards theory of generic Principal Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 661-669, April.
  49. A. El Hamidi & H. Ossman & M. Jazar, 2017. "On the convergence of alternating minimization methods in variational PGD," Computational Optimization and Applications, Springer, vol. 68(2), pages 455-472, November.
  50. Haruhiko Ogasawara, 2002. "Concise formulas for the standard errors of component loading estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 289-297, June.
  51. 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.
  52. Leo Liberti & Benedetto Manca, 2022. "Side-constrained minimum sum-of-squares clustering: mathematical programming and random projections," Journal of Global Optimization, Springer, vol. 83(1), pages 83-118, May.
  53. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
  54. Gordon Bechtel, 1973. "Nonlinear submodels of orthogonal linear models," Psychometrika, Springer;The Psychometric Society, vol. 38(3), pages 379-392, September.
  55. Thu Le & Daniel Bolt & Eric Camburn & Peter Goff & Karl Rohe, 2017. "Latent Factors in Student–Teacher Interaction Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 42(2), pages 115-144, April.
  56. Makshanov Andrey & Musaev Alexander & Grigoriev Dmitry, 2022. "Analyzing and forecasting financial series with singular spectral analysis," Dependence Modeling, De Gruyter, vol. 10(1), pages 215-224, January.
  57. Rungang Han & Yuetian Luo & Miaoyan Wang & Anru R. Zhang, 2022. "Exact clustering in tensor block model: Statistical optimality and computational limit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1666-1698, November.
  58. Torres, A. & van de Velden, M., 2005. "Perceptual mapping of mulitiple variable batteries by plotting supplementary variables in correspondence analysis of rating data," Econometric Institute Research Papers EI 2005-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  59. Mitzi Cubilla‐Montilla & Ana‐Belén Nieto‐Librero & Ma Purificación Galindo‐Villardón & Ma Purificación Vicente Galindo & Isabel‐María Garcia‐Sanchez, 2019. "Are cultural values sufficient to improve stakeholder engagement human and labour rights issues?," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 26(4), pages 938-955, July.
  60. Naoto Yamashita & Shin-ichi Mayekawa, 2015. "A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering," 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. 9(3), pages 243-266, September.
  61. Paramveer S. Dhillon & Sinan Aral, 2021. "Modeling Dynamic User Interests: A Neural Matrix Factorization Approach," Marketing Science, INFORMS, vol. 40(6), pages 1059-1080, November.
  62. D. Leventhal & A. S. Lewis, 2010. "Randomized Methods for Linear Constraints: Convergence Rates and Conditioning," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 641-654, August.
  63. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
  64. Johannes Burge & Priyank Jaini, 2017. "Accuracy Maximization Analysis for Sensory-Perceptual Tasks: Computational Improvements, Filter Robustness, and Coding Advantages for Scaled Additive Noise," PLOS Computational Biology, Public Library of Science, vol. 13(2), pages 1-32, February.
  65. Zhang Fan & Miecznikowski Jeffrey C. & Tritchler David L., 2020. "Identification of supervised and sparse functional genomic pathways," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 19(1), pages 1-27, February.
  66. Gass, S. I. & Rapcsak, T., 2004. "Singular value decomposition in AHP," European Journal of Operational Research, Elsevier, vol. 154(3), pages 573-584, May.
  67. Xin-long Luo & Zhi-jun Wu, 2011. "Least-Squares Approximations in Geometric Buildup for Solving Distance Geometry Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 580-598, June.
  68. Firoozye, Nikan & Tan, Vincent & Zohren, Stefan, 2023. "Canonical portfolios: Optimal asset and signal combination," Journal of Banking & Finance, Elsevier, vol. 154(C).
  69. Christina Yassouridis & Friedrich Leisch, 2017. "Benchmarking different clustering algorithms on functional 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(3), pages 467-492, September.
  70. Ying Guo, 2011. "A General Probabilistic Model for Group Independent Component Analysis and Its Estimation Methods," Biometrics, The International Biometric Society, vol. 67(4), pages 1532-1542, December.
  71. Jos Berge & Henk Kiers, 1993. "An alternating least squares method for the weighted approximation of a symmetric matrix," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 115-118, March.
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  73. Shimeng Huang & Henry Wolkowicz, 2018. "Low-rank matrix completion using nuclear norm minimization and facial reduction," Journal of Global Optimization, Springer, vol. 72(1), pages 5-26, September.
  74. Michal Pešta, 2016. "Unitarily invariant errors-in-variables estimation," Statistical Papers, Springer, vol. 57(4), pages 1041-1057, December.
  75. Luis Alberto Cantera-Cantera & Cristóbal Vargas-Jarillo & Sergio Isaí Palomino-Reséndiz & Yair Lozano-Hernández & Carlos Manuel Montelongo-Vázquez, 2022. "A Polynomial Fitting Problem: The Orthogonal Distances Method," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
  76. 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.
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  84. Nicolas Jouvin & Pierre Latouche & Charles Bouveyron & Guillaume Bataillon & Alain Livartowski, 2021. "Greedy clustering of count data through a mixture of multinomial PCA," Computational Statistics, Springer, vol. 36(1), pages 1-33, March.
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