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A graphical diagnostic method for assessing the rotation in factor analytical models of atmospheric pollution

机译：用于评估大气污染因子分析模型中旋转度的图形诊断方法

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摘要

Factor analytic tools such as principal component analysis (PCA) and positive matrix factorization (PMF), suffer from rotational ambiguity in the results: different solutions (factors) provide equally good fits to the measured data. The PMF model imposes non-negativity of both source profiles and source contributions in order to reduce the rotational problem. Such constraints are generally insufficient to ensure a unique solution. In the Unmix approach, edges of the multidimensional distribution of source contributions define the variable relationships in the factors. The present work extends this idea into an easy-to-use graphical procedure called G space plotting for PMF modeling. Scatter plots are created of pairs of source contribution factors. When factors are plotted in this way, unrealistic rotations appear as oblique edges that define the distribution of points away from one (or both) of the coordinate axes. With a correct rotation, the limiting edges usually coincide with the axes or lay parallel with them. Inspection of the plots helps one in choosing a realistic rotation.
机译：诸如主要成分分析（PCA）和正矩阵分解（PMF）之类的因子分析工具在结果上存在旋转歧义的问题：不同的解决方案（因子）对测量数据的拟合程度相同。 PMF模型强加了源剖面和源贡献的非负值，以减少旋转问题。这样的约束通常不足以确保独特的解决方案。在非混合方法中，源贡献的多维分布的边缘定义了因素中的变量关系。当前的工作将这一思想扩展到了一个易于使用的图形化过程，称为PMF建模的G空间图。散点图是由成对的源贡献因子创建的。当以这种方式绘制因子时，不切实际的旋转会显示为倾斜的边沿，从而定义了远离一个（或两个）坐标轴的点的分布。正确旋转后，限制边缘通常与轴重合或平行。对地块的检查有助于人们选择现实的旋转方式。

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