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The approximation of one matrix by another of lower rank

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  1. 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.
  2. Antti J Tanskanen & Jani Lukkarinen & Kari Vatanen, 2018. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-22, December.
  3. 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.
  4. Gower, John C. & Ngouenet, Roger F., 2005. "Nonlinearity effects in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 344-365, June.
  5. Walter Kristof, 1967. "Orthogonal inter-battery factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 32(2), pages 199-227, June.
  6. Marie Chavent & Vanessa Kuentz-Simonet & Jérôme Saracco, 2012. "Orthogonal rotation in PCAMIX," 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(2), pages 131-146, July.
  7. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
  8. John Leventides & George Petroulakis & Nicos Karcanias, 2016. "Distance Optimization and the Extremal Variety of the Grassmann Variety," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 1-16, April.
  9. 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.
  10. Lansangan, Joseph Ryan G. & Barrios, Erniel B., 2017. "Simultaneous dimension reduction and variable selection in modeling high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 242-256.
  11. Cui, Can & Wu, Teresa & Hu, Mengqi & Weir, Jeffery D. & Li, Xiwang, 2016. "Short-term building energy model recommendation system: A meta-learning approach," Applied Energy, Elsevier, vol. 172(C), pages 251-263.
  12. 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.
  13. Miguel Acosta, 2015. "FOMC Responses to Calls for Transparency," Finance and Economics Discussion Series 2015-60, Board of Governors of the Federal Reserve System (U.S.).
  14. Keith Poole, 1990. "Least squares metric, unidimensional scaling of multivariate linear models," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 123-149, March.
  15. Michael Greenacre, 2009. "Contribution biplots," Economics Working Papers 1162, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2011.
  16. Haedo, Christian & Mouchart, Michel, 2016. "Automatic biclustering of regions and sectors," LIDAM Discussion Papers ISBA 2016042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  17. 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.
  18. 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).
  19. 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.
  20. Haedo, Christian & Mouchart, Michel, 2018. "Automatic biclustering of regions and sectors," LIDAM Discussion Papers ISBA 2018026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  21. Veronica Piccialli & Antonio M. Sudoso & Angelika Wiegele, 2022. "SOS-SDP: An Exact Solver for Minimum Sum-of-Squares Clustering," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2144-2162, July.
  22. 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.
  23. Harold Gulliksen, 1961. "Measurement of learning and mental abilities," Psychometrika, Springer;The Psychometric Society, vol. 26(1), pages 93-107, March.
  24. Peter Schönemann, 1968. "On two-sided orthogonal procrustes problems," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 19-33, March.
  25. 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.
  26. 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.
  27. Jean-Jacques Denimal & Sergio Camiz, 2022. "Complex Principal Component Analysis: Theory and Geometrical Aspects," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 376-408, July.
  28. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2009. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," NBER Working Papers 15296, National Bureau of Economic Research, Inc.
  29. 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.
  30. Stan Lipovetsky & W. Michael Conklin, 2015. "Predictor relative importance and matching regression parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 1017-1031, May.
  31. R. Weitzman, 1963. "A factor analytic method for investigating differences between groups of individual learning curves," Psychometrika, Springer;The Psychometric Society, vol. 28(1), pages 69-80, March.
  32. 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.
  33. 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.
  34. Aldrin, Magne, 1996. "Moderate projection pursuit regression for multivariate response data," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 501-531, May.
  35. 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.
  36. 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.
  37. Marco, Nicholas & Şentürk, Damla & Jeste, Shafali & DiStefano, Charlotte C. & Dickinson, Abigail & Telesca, Donatello, 2024. "Flexible regularized estimation in high-dimensional mixed membership models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
  38. M. Perrot‐Dockès & C. Lévy‐Leduc & L. Rajjou, 2022. "Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 119-147, January.
  39. Zura Kakushadze & Willie Yu, 2020. "Machine Learning Treasury Yields," Bulletin of Applied Economics, Risk Market Journals, vol. 7(1), pages 1-65.
  40. Tuncer, Yalcin & Tanik, Murat M. & Allison, David B., 2008. "An overview of statistical decomposition techniques applied to complex systems," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2292-2310, January.
  41. 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.
  42. Peter Schönemann & Robert Carroll, 1970. "Fitting one matrix to another under choice of a central dilation and a rigid motion," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 245-255, June.
  43. 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.
  44. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
  45. Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
  46. 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.
  47. Norman Cliff, 1962. "Analytic rotation to a functional relationship," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 283-295, September.
  48. 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.
  49. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
  50. William Meredith, 1964. "Rotation to achieve factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 187-206, June.
  51. 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.
  52. Joseph Kruskal & Roger Shepard, 1974. "A nonmetric variety of linear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 39(2), pages 123-157, June.
  53. 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.
  54. 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.
  55. 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.
  56. Nikulin, Vladimir & Huang, Tian-Hsiang & Ng, Shu-Kay & Rathnayake, Suren I. & McLachlan, Geoffrey J., 2011. "A very fast algorithm for matrix factorization," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 773-782, July.
  57. 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.
  58. Tom Magerman & Bart Looy & Xiaoyan Song, 2010. "Exploring the feasibility and accuracy of Latent Semantic Analysis based text mining techniques to detect similarity between patent documents and scientific publications," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 289-306, February.
  59. Terry Gleason & Richard Staelin, 1973. "Improving the metric quality of questionnaire data," Psychometrika, Springer;The Psychometric Society, vol. 38(3), pages 393-410, September.
  60. Richard Johnson, 1966. "The minimal transformation to orthonormality," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 61-66, March.
  61. Gass, S. I. & Rapcsak, T., 2004. "Singular value decomposition in AHP," European Journal of Operational Research, Elsevier, vol. 154(3), pages 573-584, May.
  62. M. Corballis & R. Traub, 1970. "Longitudinal factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 35(1), pages 79-98, March.
  63. W. Gibson, 1962. "On the least-squares orthogonalization of an oblique transformation," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 193-195, June.
  64. Gordana Ispirova & Tome Eftimov & Barbara Koroušić Seljak, 2020. "P-NUT: Predicting NUTrient Content from Short Text Descriptions," Mathematics, MDPI, vol. 8(10), pages 1-21, October.
  65. József Kuti & Péter Galambos, 2018. "Affine Tensor Product Model Transformation," Complexity, Hindawi, vol. 2018, pages 1-12, March.
  66. 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.
  67. 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.
  68. Dray, Stéphane & Dufour, Anne-Béatrice, 2007. "The ade4 Package: Implementing the Duality Diagram for Ecologists," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 22(i04).
  69. Niels G. Waller, 2018. "Direct Schmid–Leiman Transformations and Rank-Deficient Loadings Matrices," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 858-870, December.
  70. Stanley Mulaik, 1986. "Factor analysis and Psychometrika: Major developments," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 23-33, March.
  71. Assuntina Cembalo & Rosaria Lombardo & Eric J. Beh & Gianpaolo Romano & Michele Ferrucci & Francesca M. Pisano, 2021. "Assessment of Climate Change in Italy by Variants of Ordered Correspondence Analysis," Stats, MDPI, vol. 4(1), pages 1-16, March.
  72. Firoozye, Nikan & Tan, Vincent & Zohren, Stefan, 2023. "Canonical portfolios: Optimal asset and signal combination," Journal of Banking & Finance, Elsevier, vol. 154(C).
  73. Peter Schönemann, 1966. "A generalized solution of the orthogonal procrustes problem," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 1-10, March.
  74. Nerea González-García & Ana Belén Nieto-Librero & Purificación Galindo-Villardón, 2023. "CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD," 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. 17(1), pages 5-19, March.
  75. 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.
  76. 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.
  77. Ganiere, Pierre & Chern, Wen S. & Hahn, David E., 2004. "Who Are Proponents And Opponents Of Genetically Modified Foods In The United States?," Working Papers 28315, Ohio State University, Department of Agricultural, Environmental and Development Economics.
  78. 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.
  79. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
  80. 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.
  81. 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.
  82. 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.
  83. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
  84. Zura Kakushadze & Willie Yu, 2020. "Machine Learning Treasury Yields," Papers 2003.05095, arXiv.org.
  85. 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.
  86. 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.
  87. 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.
  88. Jos Berge & Henk Kiers, 1991. "Some clarifications of the CANDECOMP algorithm applied to INDSCAL," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 317-326, June.
  89. 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.
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  93. 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.
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  120. Carmen C. Rodríguez-Martínez & Mitzi Cubilla-Montilla & Purificación Vicente-Galindo & Purificación Galindo-Villardón, 2021. "Sparse STATIS-Dual via Elastic Net," Mathematics, MDPI, vol. 9(17), pages 1-15, August.
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  122. Elvin Isufi & Andreas Loukas & Nathanael Perraudin & Geert Leus, 2018. "Forecasting Time Series with VARMA Recursions on Graphs," Papers 1810.08581, arXiv.org, revised Jul 2019.
  123. Chen Chen & Ting Kei Pong & Lulin Tan & Liaoyuan Zeng, 2020. "A difference-of-convex approach for split feasibility with applications to matrix factorizations and outlier detection," Journal of Global Optimization, Springer, vol. 78(1), pages 107-136, September.
  124. Víctor Amor‐Esteban & María Purificación Galindo‐Villardón & Isabel‐María García‐Sánchez, 2020. "Bias in composite indexes of CSR practice: An analysis of CUR matrix decomposition," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 27(4), pages 1914-1936, July.
  125. Koo, Bonchan & Chang, Seungjoon & Kwon, Hweeung, 2023. "Digital twin for natural gas infrastructure operation and management via streaming dynamic mode decomposition with control," Energy, Elsevier, vol. 274(C).
  126. Haedo, Christian & Mouchart, Michel, 2019. "Two-mode clustering through profiles of regions and sectors," LIDAM Discussion Papers ISBA 2019014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  127. Torokhti, Anatoli & Friedland, Shmuel, 2009. "Towards theory of generic Principal Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 661-669, April.
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