Consonni V, Ballabio D, Manganaro A, Mauri A, Todeschini R
Milano Chemometrics and QSAR Research Group, Department of Environmental Sciences, University of Milano-Bicocca, I-20126 Milano, Italy.
Anal Chim Acta. 2009 Aug 19;648(1):52-9. doi: 10.1016/j.aca.2009.06.035. Epub 2009 Jun 21.
This paper proposes a new method for determining the subset of variables that reproduce as well as possible the main structural features of the complete data set. This method can be useful for pre-treatment of large data sets since it allows discarding variables that contain redundant information. Reducing the number of variables often allows one to better investigate data structure and obtain more stable results from multivariate modelling methods. The novel method is based on the recently proposed canonical measure of correlation (CMC index) between two sets of variables [R. Todeschini, V. Consonni, A. Manganaro, D. Ballabio, A. Mauri, Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 1. Theory and simple chemometric applications, Anal. Chim. Acta submitted for publication (2009)]. Following a stepwise procedure (backward elimination), each variable in turn is compared to all the other variables and the most correlated is definitively discarded. Finally, a key subset of variables being as orthogonal as possible are selected. The performance was evaluated on both simulated and real data sets. The effectiveness of the novel method is discussed by comparison with results of other well known methods for variable reduction, such as Jolliffe techniques, McCabe criteria, Krzanowski approach and its modification based on genetic algorithms, loadings of the first principal component, Key Set Factor Analysis (KSFA), Variable Inflation Factor (VIF), pairwise correlation approach, and K correlation analysis (KIF). The obtained results are consistent with those of the other considered methods; moreover, the advantage of the proposed CMC method is that calculation is very quick and can be easily implemented in any software application.
本文提出了一种新方法，用于确定能够尽可能重现完整数据集主要结构特征的变量子集。该方法对于大型数据集的预处理可能很有用，因为它允许丢弃包含冗余信息的变量。减少变量数量通常能让人更好地研究数据结构，并从多元建模方法中获得更稳定的结果。这种新方法基于最近提出的两组变量之间的典型相关度量（CMC指数）[R.托德斯基尼、V.孔索尼、A.曼加纳罗、D.巴拉比奥、A.毛里，数据组之间的典型相关度量（CMC）和典型距离度量（CMD）。第1部分。理论与简单的化学计量学应用，《分析化学学报》已提交发表（2009年）]。按照逐步程序（向后消除），依次将每个变量与所有其他变量进行比较，最终丢弃相关性最高的变量。最后，选择尽可能正交的关键变量子集。在模拟数据集和真实数据集上都对性能进行了评估。通过与其他著名的变量约简方法的结果进行比较，讨论了这种新方法的有效性，这些方法包括乔利夫技术、麦凯布准则、克扎诺夫斯基方法及其基于遗传算法的改进、第一主成分的载荷、关键集因子分析（KSFA）、方差膨胀因子（VIF）、成对相关方法和K相关分析（KIF）。获得的结果与其他所考虑方法的结果一致；此外，所提出的CMC方法的优点是计算非常快速，可以很容易地在任何软件应用程序中实现。
