Data analytics using canonical correlation analysis and Monte Carlo simulation(基于正则相关分析和蒙特卡洛模拟的数据分析) 
Jeffrey M. Rickman, Yan Wang, Anthony D. Rollett, Martin P. Harmer & Charles Compson
npj Computational Materials 3, Article number: 26(2017)
doi:10.1038/s41524-017-0028-9
Published online:05 July 2017
Abstract| Full Text | PDFOPEN

摘要:正则相关（canonical correlation）分析是数据统计分析中的通用参数模型，数据包含相关或相互依赖的输入、输出变量。作为一种降维策略，它在数据分析中特别有用：通过把识别最小相关变量进行相对较少的组合，从而实现多维参数空间的简化。然而，正则相关分析仅仅提供使这些相关性最大化的变量的线性组合。考虑到这一点，本研究建立了一种多功能的基于Monte-Carlo的方法，可用于确定描述输入/输出变量强相关性的非线性函数。通过两个材料科学领域重要实验研究证明了此方法可显著增强变量相关性，（1）确定了与掺杂多晶氧化铝相关的加工和微结构变量间的相互依赖性，（2）将微结构描述符与基于CuInSe2吸收体的薄膜太阳能电池的电器和光电性能关联起来。最后，我们还描述了本方法如何有助于实验规划和过程控制。 　　

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 descriptors 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. 

Editorial Summary

Data analytics: Non-linear model for establishing correlations (数据分析：建立相关性的非线性模型) 

该研究提出了一种用于定量化非线性关系的方法，为理解材料微结构-性质关系提供基础。正则相关分析就是用于量化两组变量之间关系的常用技术，但当关系是非线性时，该技术通常就难办了。现在来自美国Lehigh大学的Jeffrey Rickman及其领导的国际团队，提出了一个基于Monte-Carlo的扩展正则相关分析，可用来解决有潜在非线性变量依赖性的情况。他们通过建立描述陶瓷氧化物中异常晶粒生长的变量之间的相关性，和建立微结构与某些太阳能电池的电气和光电性能最重要变量之间的相关性，来证实上述相关分析方法的可靠性，并揭示了该方法所适用的材料系统范围。

A method for quantifying non-linear relationships provides insight into the connections between microstructure and properties of materials. Canonical correlation analysis is a common technique used to quantify the relationship between two sets of variables but it is often difficult to apply when the relationships are non-linear. An international team of researchers led by Jeffrey Rickman from Lehigh University now present a Monte-Carlo-based extension of canonical correlation analysis that can be applied to scenarios where non-linear variable dependencies are likely. They demonstrate this approach by establishing correlations between the variables responsible for abnormal grain growth in a ceramic oxide, as well as the variables that are most important in connecting the microstructure to the electrical and optoelectronic properties of certain solar cells, showing the range of materials systems that this approach could be used for.