Monte-Carlo扩展正则相关分析：非线性模型的建立

2017 年 8 月 25 日 知社学术圈 npj CM

海归学者发起的公益学术平台

分享信息，整合资源

交流学术，偶尔风月

正则相关分析是数据统计分析中的通用参数模型，是用于量化两组变量之间关系的常用技术，在数据分析中特别有用，可作为一种降维策略，识别最小相关变量的较少的组合来简化复杂多维的参数空间。然而，正则相关分析遇到非线性组合时就会无所适从。对此，来自美国Lehigh大学的Jeffrey Rickman及其领导的国际团队，提出了基于Monte-Carlo的扩展正则相关分析方法，用于确定输入/输出变量强相关性的非线性函数，解决有潜在非线性变量依赖性的问题。他们通过材料科学领域两个重要实验研究，验证了该方法可显著增强变量间的相关性。实验研究表明（1）建立掺杂多晶氧化铝相关的加工和微结构变量之间的相互依赖性；（2）确定CuInSe2吸收体的薄膜太阳能电池材料的微结构表征与电学/光电性能之间的关系。最后，他们还描述了该方法如何有助于实验规划和过程控制，并揭示了该方法所适用的材料体系范围。该文近期发表于npj Computational Materials 3: 26 (2017); doi:10.1038/s41524-017-0028-9; 标题与摘要如下，论文PDF文末点击阅读原文可以获取。

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

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.