Data analytics using canonical correlation analysis and Monte Carlo simulation
Source abstract
Abstract
Abstract A canonical correlation analysis is a generic parametric model used in the statistical analysis of data involving interrelated or interdependent input and output variables. It is especially useful in data analytics as a dimensional reduction strategy that simplifies a complex, multidimensional parameter space by identifying a relatively few combinations of variables that are maximally correlated. One shortcoming of the canonical correlation analysis, however, is that it provides only a linear combination of variables that maximizes these correlations. With this in mind, we describe here a versatile, Monte-Carlo based methodology that is useful in identifying non-linear functions of the variables that lead to strong input/output correlations. We demonstrate that our approach leads to a substantial enhancement of correlations, as illustrated by two experimental applications of substantial interest to the materials science community, namely: (1) determining the interdependence of processing and microstructural variables associated with doped polycrystalline aluminas, and (2) relating microstructural decriptors to the electrical and optoelectronic properties of thin-film solar cells based on CuInSe2 absorbers. Finally, we describe how this approach facilitates experimental planning and process control.
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Research context
OpenAlex topics: Chalcogenide Semiconductor Thin Films · Machine Learning in Materials Science · Semiconductor materials and interfaces
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References (35)
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1. Samudrala, S., Rajan, K. & Ganapathysubramanian, B. in Informatics for Materials Science and Engineering (ed. Rajan, K.) (Elsevier, 2013).
2. Lee, J. A. & Verleysen, M. Nonlinear Dimensionality Reduction (Springer, 2007).10.1007/978-0-387-39351-3 ↗
3. Jackson, J. E. A User’s Guide to Principal Components (John Wiley and Sons, 2003).
4. Wu, K., Natarajan, B., Morkowchuk, L., Krein, M. & Breneman, C. M. in Informatics for Materials Science and Engineering (ed. Rajan, K.) (Elsevier, 2013).
5. Huang, W. & Yin, H. in Intelligent Data Engineering and Automated Learning-IDEAL 2009 (eds Corchado, E. & Yin, H.) (Springer-Verlag, 2009).
6. Meredith, W. & Millsap, R. E. On component analysis. Psychometrika 50, 495–507 (1985).10.1007/BF02296266 ↗
7. Gnanadesikan, R. & Wilk, M. B. in Multivariate Analysis II (ed. Krishnaiah, P. R.) (Academic Press, 1969).
8. Knapp, T. R. Canonical correlation analyis: a general parametric significance-testing system. Psych. Bull 85, 410–416 (1978).10.1037/0033-2909.85.2.410 ↗
9. Burges, C. J. C. Dimension reduction: a guided tour. Found. Trends Mach. Learn. 2, 275–365 (2009).10.1561/2200000002 ↗
10. Akaho, S. in International Meeting of Psychometric Society (Osaka, Japan, 2001).
11. Balakrishnan, S., Puniyani, K. & Lafferty, J. Sparse additive functional and kernel CCA, in Proc. 29th International Conference on Machine Learning (Edinburgh, 2012).
12. Ivakhnenko, A. G. & Ivakhnenko, G. A. The review of problems solvable by algorithms of the group method of data handling (GMDH). Pattern Recogn. Image Anal 5, 527–535 (1995).
13. Schmidhuber, J. Deep learning in neural networks: an overview. Neural Networks 61, 85–117 (2015).10.1016/j.neunet.2014.09.003 ↗
14. Jobson, J. D. Applied Multivariate Data Analysis, Vol. II (Springer-Verlag, 1992).10.1007/978-1-4612-0921-8 ↗
15. Gittins, R. Canonical Analysis: A Review With Applications In Ecology (Springer-Verlag, 1985).10.1007/978-3-642-69878-1 ↗
16. Hartmann, A. K. & Weigt, M. Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics (Wiley-VCH, 2005).10.1002/3527606734 ↗
17. Dehuri, S., Coello, C., Cho, S. -B. & Ghosh, A. in Swarm Intelligence for Multi-Objective Problems in Data Mining (eds Coello, C., Dehuri, S. and Ghosh, S.) 115–155 (Springer-Verlag, 2009).10.1007/978-3-642-03625-5_6 ↗
18. Baker, G. A. & Graves-Morris, P. Padé Approximants 2nd edn, (Cambridge University Press, 1996).10.1017/CBO9780511530074 ↗
19. Turut, V. & Bayram, M. Rational approximations for solving Cauchy problems. New Trend. Math. Sci. 4, 254–262 (2016).10.20852/ntmsci.2016320380 ↗
20. Cuyt, A. A review of multivariate Padé approximation theory. J. Comp. Appl. Math 12,13, 221–232 (1985).10.1016/0377-0427(85)90019-6 ↗
21. Thorndike, R. M. Correlational Procedures for Research (Gardner Press, 1978).
22. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in Fortran: The Art of Scientific Computing 2nd edn, (Cambridge University Press, 1992).
23. Gentle, J. E. Matrix Algebra: Theory, Computations and Applications in Statistics (Springer, 2007).10.1007/978-0-387-70873-7 ↗
24. Rollett, A. D., Srolovitz, D. J. & Anderson, M. P. Simulation and theory of abnormal grain growth-anisotropic grain boundary energies and mobilities. Acta Metall 37, 1127–1240 (1989).
25. Mullins, W. W. & Viñals, J. Linear bubble model of abnormal grain growth. Acta Mater. 50, 2945–2954 (2002).10.1016/S1359-6454(02)00121-0 ↗
26. Handwerker, C. A., Morris, P. A. & Coble, R. L. Effects of chemical inhomogeneities on grain growth and microstructure in Al2O3. J. Am. Ceram. Soc. 72, 130–136 (1989).10.1111/j.1151-2916.1989.tb05965.x ↗
27. Lawrence, A., Rickman, J. M., Harmer, M. P. & Rollett, A. D. Parsing abnormal grain growth. Acta Mater. 103, 681–687 (2016).10.1016/j.actamat.2015.10.034 ↗
28. Cho, J., Wang, C. M., Chan, H. M., Rickman, J. M. & Harmer, M. P. Improved tensile creep properties of yttrium- and lanthanum-doped alumina: a solid solution effect. J. Mater. Res. 16, 425–429 (2001).10.1557/JMR.2001.0064 ↗
29. Wang, C.-M., Cho, J., Chan, H. M., Harmer, M. P. & Rickman, J. M. Influence of dopant concentration on creep properties of Nd2O3-doped alumina. J. Amer. Ceram. Soc 84, 1010–1016 (2001).10.1111/j.1151-2916.2001.tb00783.x ↗
30. Rickman, J. M., LeSar, R. & Srolovitz, D. J. Solute effects on dislocation glide in metals. Acta Mater. 51, 1199 (2003).10.1016/S1359-6454(02)00304-X ↗
31. Jackson, P. et al. Effects of heavy alkali elements in Cu(In,Ga)Se2 solar cells with efficiencies up to 22.6%. Phys. Stat. Sol. (RRL), doi:10.1002/pssr.201600199.10.1002/pssr.201600199 ↗
32. Rao, U., Taretto, K. & Siebentritt, S. Grain boundaries in Cu(In,Ga)(Se,S)2 thin-film solar cells. Appl. Phys. A 96, 221 (2009).10.1007/s00339-008-4978-0 ↗
33. Abou-Ras, D. et al. Grain-boundary character distribution and correlations with electrical and optoelectronic properties of CuInSe2 thin films. Acta Metall 118, 244–252 (2016).
34. Barcikowski, R. S. & Stevens, J. P. A Monte Carlo study of the stability of canonical correlations, canonical weights and canonical variate-variable correlations. Multivariate Behav. Res. 10, 353–364 (1975).10.1207/s15327906mbr1003_8 ↗
35. Rao, M. & Berne, B. J. On the force-bias Monte Carlo simulation of simple liquids. J. Chem. Phys. 71, 129–132 (1979).10.1063/1.438111 ↗