D-CCA: A Decomposition-Based Canonical Correlation Analysis for High-Dimensional Datasets

References

• Ahn, S. C., and Horenstein, A. R. (2013), “Eigenvalue Ratio Test for the Number of Factors,” Econometrica, 81, 1203–1227.
   Web of Science ®Google Scholar
• Bai, J. (2003), “Inferential Theory for Factor Models of Large Dimensions,” Econometrica, 71, 135–171. DOI: 10.1111/1468-0262.00392.
   Web of Science ®Google Scholar
• Bai, J., and Ng, S. (2002), “Determining the Number of Factors in Approximate Factor Models,” Econometrica, 70, 191–221. DOI: 10.1111/1468-0262.00273.
   Web of Science ®Google Scholar
• Bai, J., and Ng, S. (2008), “Large Dimensional Factor Analysis,” Foundations and Trends in Econometrics, 3, 89–163.
   Google Scholar
• Barigozzi, M., Hallin, M., and Soccorsi, S. (2018), “Identification of Global and Local Shocks in International Financial Markets via General Dynamic Factor Models,” Journal of Financial Econometrics, https://doi.org/10.1093/jjfinec/nby006.
   Web of Science ®Google Scholar
• Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
   Web of Science ®Google Scholar
• Björck, A., and Golub, G. H. (1973), “Numerical Methods for Computing Angles Between Linear Subspaces,” Mathematics of Computation, 27, 579–594. DOI: 10.2307/2005662.
   Web of Science ®Google Scholar
• Cabanski, C. R., Qi, Y., Yin, X., Bair, E., Hayward, M. C., Fan, C., Li, J., Wilkerson, M. D., Marron, J. S., Perou, C. M., and Hayes, D. N. (2010), “SWISS MADE: Standardized Within Class Sum of Squares to Evaluate Methodologies and Dataset Elements,” PLoS ONE, 5, e9905. DOI: 10.1371/journal.pone.0009905.
   PubMed Web of Science ®Google Scholar
• Chamberlain, G., and Rothschild, M. (1983), “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,” Econometrica, 51, 1281–1304. DOI: 10.2307/1912275.
   Web of Science ®Google Scholar
• Chen, M., Gao, C., Ren, Z., and Zhou, H. H. (2013), “Sparse CCA via Precision Adjusted Iterative Thresholding,” arXiv no. 1311.6186.
   Google Scholar
• Ciriello, G., Gatza, M. L., Beck, A. H., Wilkerson, M. D., Rhie, S. K., Pastore, A., Zhang, H., McLellan, M., Yau, C., Kandoth, C., and Bowlby, R. (2015), “Comprehensive Molecular Portraits of Invasive Lobular Breast Cancer,” Cell, 163, 506–519. DOI: 10.1016/j.cell.2015.09.033.
   PubMed Web of Science ®Google Scholar
• Comon, P., and Jutten, C. (2010), Handbook of Blind Source Separation: Independent Component Analysis and Applications, Oxford: Academic Press.
   Google Scholar
• DiCiccio, C. J., and Romano, J. P. (2017), “Robust Permutation Tests for Correlation and Regression Coefficients,” Journal of the American Statistical Association, 112, 1211–1220. DOI: 10.1080/01621459.2016.1202117.
   Web of Science ®Google Scholar
• Fan, J., Liao, Y., and Mincheva, M. (2013), “Large Covariance Estimation by Thresholding Principal Orthogonal Complements,” Journal of the Royal Statistical Society, Series B, 75, 603–680. DOI: 10.1111/rssb.12016.
   Google Scholar
• Feng, Q., Jiang, M., Hannig, J., and Marron, J. (2018), “Angle-Based Joint and Individual Variation Explained,” Journal of Multivariate Analysis, 166, 241–265. DOI: 10.1016/j.jmva.2018.03.008.
   Web of Science ®Google Scholar
• Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2000), “The Generalized Dynamic-Factor Model: Identification and Estimation,” Review of Economics and Statistics, 82, 540–554. DOI: 10.1162/003465300559037.
   Web of Science ®Google Scholar
• Forni, M., Hallin, M., Lippi, M., and Zaffaroni, P. (2017), “Dynamic Factor Models With Infinite-Dimensional Factor Space: Asymptotic Analysis,” Journal of Econometrics, 199, 74–92. DOI: 10.1016/j.jeconom.2017.04.002.
   Web of Science ®Google Scholar
• Fukumizu, K., Bach, F. R., and Gretton, A. (2007), “Statistical Consistency of Kernel Canonical Correlation Analysis,” Journal of Machine Learning Research, 8, 361–383.
   Web of Science ®Google Scholar
• Gao, C., Ma, Z., Ren, Z., and Zhou, H. H. (2015), “Minimax Estimation in Sparse Canonical Correlation Analysis,” The Annals of Statistics, 43, 2168–2197. DOI: 10.1214/15-AOS1332.
   Web of Science ®Google Scholar
• Gao, C., Ma, Z., and Zhou, H. H. (2017), “Sparse CCA: Adaptive Estimation and Computational Barriers,” The Annals of Statistics, 45, 2074–2101. DOI: 10.1214/16-AOS1519.
   Web of Science ®Google Scholar
• Hallin, M., and Liška, R. (2011), “Dynamic Factors in the Presence of Blocks,” Journal of Econometrics, 163, 29–41. DOI: 10.1016/j.jeconom.2010.11.004.
   Web of Science ®Google Scholar
• Hotelling, H. (1936), “Relations Between Two Sets of Variates,” Biometrika, 28, 321–377. DOI: 10.1093/biomet/28.3-4.321.
   Web of Science ®Google Scholar
• Huang, H. (2017), “Asymptotic Behavior of Support Vector Machine for Spiked Population Model,” Journal of Machine Learning Research, 18, 1–21.
   Web of Science ®Google Scholar
• Kettenring, J. R. (1971), “Canonical Analysis of Several Sets of Variables,” Biometrika, 58, 433–451. DOI: 10.1093/biomet/58.3.433.
   Web of Science ®Google Scholar
• Koboldt, D., Fulton, R., McLellan, M., Schmidt, H., Kalicki-Veizer, J., McMichael, J., Fulton, L., Dooling, D., Ding, L., Mardis, E. R., and Wilson, R. K. (2012), “Comprehensive Molecular Portraits of Human Breast Tumours,” Nature, 490, 61–70. DOI: 10.1038/nature11412.
   PubMed Web of Science ®Google Scholar
• Kuligowski, J., Pérez-Guaita, D., Sánchez-Illana, Á., León-González, Z., de la Guardia, M., Vento, M., Lock, E. F., and Quintás, G. (2015), “Analysis of Multi-source Metabolomic Data Using Joint and Individual Variation Explained (JIVE),” Analyst, 140, 4521–4529. DOI: 10.1039/C5AN00706B.
   PubMed Web of Science ®Google Scholar
• Lock, E. F., Hoadley, K. A., Marron, J. S., and Nobel, A. B. (2013), “Joint and Individual Variation Explained (JIVE) for Integrated Analysis of Multiple Data Types,” Annals of Applied Statistics, 7, 523–542. DOI: 10.1214/12-AOAS597.
   PubMed Web of Science ®Google Scholar
• Löfstedt, T., and Trygg, J. (2011), “OnPLS—A Novel Multiblock Method for the Modelling of Predictive and Orthogonal Variation,” Journal of Chemometrics, 25, 441–455.
   Web of Science ®Google Scholar
• Nadakuditi, R. R., and Silverstein, J. W. (2010), “Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples,” IEEE Journal of Selected Topics in Signal Processing, 4, 468–480. DOI: 10.1109/JSTSP.2009.2038310.
   Web of Science ®Google Scholar
• O’Connell, M. J., and Lock, E. F. (2016), “R.JIVE for Exploration of Multi-source Molecular Data,” Bioinformatics, 32, 2877–2879. DOI: 10.1093/bioinformatics/btw324.
   PubMed Web of Science ®Google Scholar
• Onatski, A. (2010), “Determining the Number of Factors From Empirical Distribution of Eigenvalues,” The Review of Economics and Statistics, 92, 1004–1016. DOI: 10.1162/REST_a_00043.
   Web of Science ®Google Scholar
• Parker, J. S., Mullins, M., Cheang, M. C. U., Leung, S., Voduc, D., Vickery, T., Davies, S., Fauron, C., He, X., Hu, Z., Quackenbush, J. F., Stijleman, I. J., Palazzo, J., Marron, J. S., Nobel, A. B., Mardis, E., Nielsen, T. O., Ellis, M. J., Perou, C. M., and Bernard, P. S. (2009), “Supervised Risk Predictor of Breast Cancer Based on Intrinsic Subtypes,” Journal of Clinical Oncology, 27, 1160–1167. DOI: 10.1200/JCO.2008.18.1370.
   PubMed Web of Science ®Google Scholar
• Ross, S. A. (1976), “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, 13, 341–360. DOI: 10.1016/0022-0531(76)90046-6.
   Web of Science ®Google Scholar
• Schouteden, M., Van Deun, K., Wilderjans, T. F., and Van Mechelen, I. (2014), “Performing DISCO-SCA to Search for Distinctive and Common Information in Linked Data,” Behavior Research Methods, 46, 576–587.
   PubMed Web of Science ®Google Scholar
• Smilde, A. K., Mage, I., Naes, T., Hankemeier, T., Lips, M. A., Kiers, H. A. L., Acar, E., and Bro, R. (2017), “Common and Distinct Components in Data Fusion,” Journal of Chemometrics, 31, e2900. DOI: 10.1002/cem.2900.
   Web of Science ®Google Scholar
• Song, Y., Schreier, P. J., Ramírez, D., and Hasija, T. (2016), “Canonical Correlation Analysis of High-Dimensional Data With Very Small Sample Support,” Signal Processing, 128, 449–458. DOI: 10.1016/j.sigpro.2016.05.020.
   Web of Science ®Google Scholar
• Stock, J. H., and Watson, M. W. (2002), “Forecasting Using Principal Components From a Large Number of Predictors,” Journal of the American Statistical Association, 97, 1167–1179. DOI: 10.1198/016214502388618960.
   Web of Science ®Google Scholar
• Székely, G. J., Rizzo, M. L., and Bakirov, N. K. (2007), “Measuring and Testing Dependence by Correlation of Distances,” The Annals of Statistics, 35, 2769–2794. DOI: 10.1214/009053607000000505.
   Web of Science ®Google Scholar
• Trygg, J. (2002), “O2-PLS for Qualitative and Quantitative Analysis in Multivariate Calibration,” Journal of Chemometrics, 16, 283–293. DOI: 10.1002/cem.724.
   Web of Science ®Google Scholar
• van der Kloet, F., Sebastian-Leon, P., Conesa, A., Smilde, A., and Westerhuis, J. (2016), “Separating Common From Distinctive Variation,” BMC Bioinformatics, 17, S195.
   PubMed Web of Science ®Google Scholar
• Van Essen, D. C., Smith, S. M., Barch, D. M., Behrens, T. E., Yacoub, E., and Ugurbil, K. (2013), “The WU-Minn Human Connectome Project: An Overview,” NeuroImage, 80, 62–79. DOI: 10.1016/j.neuroimage.2013.05.041.
   PubMed Web of Science ®Google Scholar
• Vershynin, R. (2012), “Introduction to the Non-asymptotic Analysis of Random Matrices,” in Compressed Sensing, Cambridge: Cambridge University Press, pp. 210–268.
   Google Scholar
• Wang, W., and Fan, J. (2017), “Asymptotics of Empirical Eigenstructure for High Dimensional Spiked Covariance,” The Annals of Statistics, 45, 1342–1374. DOI: 10.1214/16-AOS1487.
   PubMed Web of Science ®Google Scholar
• Yu, Q., Risk, B. B., Zhang, K., and Marron, J. (2017), “Jive Integration of Imaging and Behavioral Data,” NeuroImage, 152, 38–49. DOI: 10.1016/j.neuroimage.2017.02.072.
   PubMed Web of Science ®Google Scholar
• Zhou, G., Cichocki, A., Zhang, Y., and Mandic, D. P. (2016), “Group Component Analysis for Multiblock Data: Common and Individual Feature Extraction,” IEEE Transactions on Neural Networks and Learning Systems, 27, 2426–2439. DOI: 10.1109/TNNLS.2015.2487364.
   PubMed Web of Science ®Google Scholar