Data analytics using canonical correlation analysis and Monte Carlo simulation

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 CuInSe 2 absorbers. Finally, we describe how this approach facilitates experimental planning and process control.

Review of grain boundary complexion engineering: Know your boundaries

“…In materials science applications, however, we need to extract the anomalies or extreme events, like abnormal grain growth. Lawrence et al have recently formulated useful criteria (ie, metrics) by employing canonical correlation analysis to determine which processing variables are most responsible for abnormal grain growth (see Appendix ). More specifically, this analysis identified the combination of processing variables that was most correlated with the abnormality metrics.…”

Materials informatics for the screening of multi-principal elements and high-entropy alloys

“…As noted in the “Introduction” section, a CCA and its relative, a Monte Carlo CCA, have been used in a very different context to establish correlations between ceramic powder chemistry and the resulting microstructure of a dense, sintered ceramic. A similar CCA analysis has also been used to relate the microstructure to the optoelectronic properties of thin-film solar cells 22 . Thus, in this context, the CCA can also be generalized to identify alloys having other useful thermomechanical and kinetic properties (e.g., yield strength, electrical conductivity, corrosion resistance) or, as described above, to Pareto-optimize multiple properties simultaneously using a multi-objective GA.…”

“…Moreover, the eigenvectors corresponding to the maximum eigenvalue are the desired canonical variates that maximize the correlation. We note that the CCA methodology has been extended to identify non-linear variable combinations that are highly correlated 22,50,51 .…”

“…In particular, by combining a multiple regression analysis or its generalization, a canonical correlation analysis (CCA), with a genetic algorithm (GA) optimization strategy, we will explore systematically the HE alloy chemistry/composition space to highlight those alloys that have beneficial mechanical properties (e.g., high hardness). A CCA is a very general technique for quantifying relationships between two sets of variables, most parametric tests of significance being essentially special cases of CCA 20 , and it has been used recently to: explore, for example, correlations between ceramic powder chemistry and the resulting microstructure of a dense, sintered ceramic 21,22 . In this context, a GA is employed to construct many virtual candidate alloys that evolve from one generation to the next by processes that mimic reproduction and mutation, and in which survival to the next generation is dependent upon a measure of fitness.…”

Integrating multi-OMICS data through sparse Canonical Correlation Analysis for predicting complex traits: A comparative study

“…The focus of this paper is on Canonical Correlation Analysis (CCA), an intermediate integrative approach proposed by Hotelling [1936]. CCA and its variations have been applied in various disciplines, including personality assessment [Sherry and Henson, 2005], material science [Rickman et al, 2017], photogrammetry [Vestergaard and Nielsen, 2015], cardiology [Jia et al, 2019], singlecell analysis [Butler et al, 2018].…”