An intuitive and practical way to control chemical equivalence of secondary metabolites in herbal materials based on chromatographic fingerprints deserves a thorough discussion, yet it is relatively unexplored. For the first time, we propose a mixture of three similarity indices, the congruence coefficient, the average of the peak area ratios, and the larger value between the maximum peak area ratio and the reciprocal of the minimum peak area ratio, to make up for the weak points of some widely used similarity indices and to evaluate the chemical equivalence of two fingerprints from various perspectives. The three similarity values are fed into a three-dimensional kernel density estimation to determine the quality of herbal materials. This estimation enables precise detection of anomalies in the absence of prior quality determination experience. Forty Atractylodes samples similar in appearance and indiscriminately used for medical purposes were used to demonstrate the effectiveness of the developed approach. After a reference sample was postulated, a quality assessment of the 40 samples was performed using the three similarity values and the estimated kernel density. The samples that were judged by the developed approach to be of good quality were compared with those chosen by the most popular approach using decision criterion of a single similarity index. The benefits of the proposed approach were evident in that the qualified samples had the composition ratio and individual concentrations of multi-components closer to those of the reference in general, and their inter-sample deviation was significantly smaller.

中文翻译：

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结合三个相似指数和三维核密度估计，使用色谱指纹图评估草药材料的化学等效性

一种基于色谱指纹图谱控制草药材料中次生代谢物化学等效性的直观而实用的方法值得深入讨论，但相对来说还没有被探索。我们首次提出了三个相似性指标的混合，即同余系数、峰面积比的平均值以及最大峰面积比与最小峰面积比的倒数之间的较大值，以弥补一些广泛使用的相似性指数的弱点，并从不同的角度评估两个指纹的化学等效性。这三个相似度值被输入到三维核密度估计中，以确定草药材料的质量。这种估计能够在没有先前质量确定经验的情况下精确检测异常。四十个外观相似且不加区别地用于医疗目的的白术样品被用来证明所开发方法的有效性。在假定参考样本后，使用三个相似值和估计的核密度对 40 个样本进行质量评估。使用单一相似性指数的决策标准，将被开发的方法判断为质量好的样本与最流行的方法选择的样本进行比较。所提出的方法的好处是显而易见的，即合格样品的组成比和多组分的单个浓度通常更接近参考样品，并且它们的样品间偏差显着更小。