Orthogonal canonical correlation analysis and applications

References

• P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms On Matrix Manifolds, Princeton University Press, Princeton, NJ, 2008.
   Google Scholar
• Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (eds.), Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia, PA, 2000.
   Google Scholar
• D. Chu, L. Liao, M.K. Ng, and X. Zhang, Sparse canonical correlation analysis: new formulation and algorithm, IEEE Trans. Pattern Anal. Mach. Intell. 35(12) (2013), pp. 3050–3065. doi: 10.1109/TPAMI.2013.104
   PubMed Web of Science ®Google Scholar
• C. Cortes and M. Mohri, AUC optimization vs. error rate minimization, in Advances in Neural Information Processing Systems 16, S. Thrun, L.K. Saul, and B. Scholkopf, eds., 2004, pp. 313–320.
   Google Scholar
• J.P. Cunningham and Z. Ghahramani, Linear dimensionality reduction: survey, insights, and generalizations, J. Mach. Learning Res. 16 (2015), pp. 2859–2900.
   Web of Science ®Google Scholar
• K. Dembszynski, W. Waegeman, W. Cheng, and E. Hüllermeier, On label dependence in multilabel classification, LastCFP: ICML Workshop on Learning from Multi-label data, Ghent University, KERMIT, Department of Applied Mathematics, Biometrics and Process Control, 2010.
   Google Scholar
• S. Džeroski, D. Demšar, and J. Grbović, Predicting chemical parameters of river water quality from bioindicator data, Appl. Intell. 13(1) (2000), pp. 7–17. doi: 10.1023/A:1008323212047
   Web of Science ®Google Scholar
• A. Edelman, T.A. Arias, and S.T. Smith, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl. 20(2) (1999), pp. 303–353. doi: 10.1137/S0895479895290954
   Web of Science ®Google Scholar
• R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin, Liblinear: A library for large linear classification, J. Mach. Learn. Res. 9(Aug) (2008), pp. 1871–1874.
   Google Scholar
• B. Gao, X. Liu, X.J. Chen, and Y. Yuan, A new first-order algorithmic framework for optimization problems with orthogonality constraints, SIAM J. Optim. 28(1) (2018), pp. 302–332. doi: 10.1137/16M1098759
   Web of Science ®Google Scholar
• B. Gao, X. Liu, and Y. Yuan, First-order algorithms for optimization problems with orthogonality constraints, Oper. Res. Trans. 21(4) (2017), pp. 57–68.
   Google Scholar
• G.H. Golub and C.F. Van Loan, Matrix Computations, 4th ed., Johns Hopkins University Press, Baltimore, MD, 2013.
   Google Scholar
• D.R. Hardoon, S. Szedmak, and J. Shawe-Taylor, Canonical correlation analysis: an overview with application to learning methods, Neural Comput. 16(12) (2004), pp. 2639–2664. doi: 10.1162/0899766042321814
   PubMed Web of Science ®Google Scholar
• B. Hariharan, L. Zelnik-Manor, M. Varma, and S. Vishwanathan, Large scale max-marginmultilabel classification with priors, in Proceedings of the 27th International Conference on Machine Learning, J. Fürnkranz and T. Joachims, eds., Omnipress, Madison, WI, 2010, pp. 423–430.
   Google Scholar
• E. Hatzikos, G. Tsoumakas, G. Tzanisand, N. Bassiliades, and I. Vlahavas, An empirical study on sea water quality prediction, Knowl. Based Syst. 21(6) (2008), pp. 471–478. doi: 10.1016/j.knosys.2008.03.005
   Web of Science ®Google Scholar
• H. Hotelling, Relations between two sets of variates, Biometrika 28(3-4) (1936), pp. 321–377. doi: 10.1093/biomet/28.3-4.321
   Google Scholar
• J. Hu, A. Milzarek, Z. Wen, and Y. Yuan, Adaptive quadratically regularized Newton method for Riemannian optimization, SIAM J. Matrix Anal. Appl. 39 (2018), pp. 1181–1207. doi: 10.1137/17M1142478
   Web of Science ®Google Scholar
• B. Jiang and Y.-H. Dai, A framework of constraint preserving update schemes for optimization on stiefel manifold, Math. Program. 153 (2015), pp. 535–575. doi: 10.1007/s10107-014-0816-7
   Web of Science ®Google Scholar
• A. Karalič and I. Bratko, First order regression, Mach. Learn. 26(2-3) (1997), pp. 147–176. doi: 10.1023/A:1007365207130
   Web of Science ®Google Scholar
• L. Mackey, Deflation methods for sparse PCA, in Advances in Neural Information Processing Systems 21, D. Koller, D. Schuurmans, Y. Bengio and L. Bottou, eds., NIPS, 2008, pp. 1017–1024.
   Google Scholar
• R.J. Muirhead, Aspects of Multivariate Statistical Theory, 2nd ed., Wiley, New York, NY, 2005.
   Google Scholar
• J. Nocedal and S. Wright, Numerical Optimization, 2nd ed., Springer, Berlin, 2006.
   Google Scholar
• G. Rong, C. Jin, S. Kakade, and P.N.A. Sidford, Efficient algorithms for large-scale generalized eigenvector computation and canonical correlation analysis, in Proceedings of the 33rd International Conference on Machine Learning, M. Balcan and K. Weinberger, eds., JMLR, 2016, pp. 2741–2750.
   Google Scholar
• X. Shen, Q. Sun, and Y. Yuan, Orthogonal canonical correlation analysis and its application in feature fusion, in Proceedings of the 16th International Conference on Information Fusion, IEEE, Istanbul, 2013, pp. 151–157.
   Google Scholar
• E. Spyromitros-Xioufis, G. Tsoumakas, W. Groves, and I. Vlahavas, Multi-target regression via input space expansion: treating targets as inputs, Mach. Learn. 104(1) (2016), pp. 55–98. doi: 10.1007/s10994-016-5546-z
   Web of Science ®Google Scholar
• L. Sun, S. Ji, and J. Ye, A least squares formulation for canonical correlation analysis, in Proceeding of the 25th International Conference on Machine learning, A. McCallum and S. Roweis eds., ACM, New York, 2008, pp. 1024–1031.
   Google Scholar
• Q.-S. Sun, S.-G. Zeng, Y. Liu, P.-A. Heng, and D.-S. Xia, A new method of feature fusion and its application in image recognition, Pattern. Recognit. 38(12) (2005), pp. 2437–2448. doi: 10.1016/j.patcog.2004.12.013
   Web of Science ®Google Scholar
• W. Sun and Y. Yuan, Optimization Theory and Methods, Springer, Berlin, 2006.
   Google Scholar
• A. Tsanas and A. Xifara, Accurate quantitative estimation of energy performance of residential buildings using statistical machine learning tools, Energy Build. 49 (2012), pp. 560–567. doi: 10.1016/j.enbuild.2012.03.003
   Web of Science ®Google Scholar
• Z. Wen and W. Yin, A feasible method for optimization with orthogonality constraints, Math. Program. 142(1-2) (2013), pp. 397–434. doi: 10.1007/s10107-012-0584-1
   Web of Science ®Google Scholar
• I-C. Yeh, Modeling slump flow of concrete using second-order regressions and artificial neural networks, Cem. Concr. Compos. 29(6) (2007), pp. 474–480. doi: 10.1016/j.cemconcomp.2007.02.001
   Web of Science ®Google Scholar
• L.-H. Zhang and R.-C. Li, Maximization of the sum of the trace ratio on the Stiefel manifold, I: theory, Sci. China Math. 57(12) (2014), pp. 2495–2508. doi: 10.1007/s11425-014-4824-0
   Web of Science ®Google Scholar
• L.-H. Zhang and R.-C. Li, Maximization of the sum of the trace ratio on the Stiefel manifold, II: computation, Sci. China Math. 58(7) (2015), pp. 1549–1566. doi: 10.1007/s11425-014-4825-z
   Web of Science ®Google Scholar