This paper explores the internal structure of two quantum mechanics datasets
(QM7b, QM9), composed of several thousands of organic molecules and described
in terms of electronic properties. Understanding the structure and
characteristics of this kind of data is important when predicting the atomic
composition from the properties in inverse molecular designs. Intrinsic
dimension analysis, clustering, and outlier detection methods were used in the
study. They revealed that for both datasets the intrinsic dimensionality is
several times smaller than the descriptive dimensions. The QM7b data is
composed of well defined clusters related to atomic composition. The QM9 data
consists of an outer region predominantly composed of outliers, and an inner
core region that concentrates clustered, inliner objects. A significant
relationship exists between the number of atoms in the molecule and its
outlier/inner nature. Despite the structural differences, the predictability of
variables of interest for inverse molecular design is high. This is exemplified
with models estimating the number of atoms of the molecule from both the
original properties, and from lower dimensional embedding spaces.

两个量子力学数据集（QM7b 和 QM9）的内部结构被探索，研究了它们在电子性质方面的描述。通过内部维度分析、聚类和异常值检测方法，研究揭示了这两个数据集的内在维度远远小于描述维度。QM7b 数据由与原子组成相关的明确定义的聚类组成，而 QM9 数据由以异常值为主的外部区域和集中聚类的内核区域组成。分子中的原子数量与异常值 / 内部性质之间存在显著关系。尽管结构上存在差异，但逆向分子设计的目标变量的可预测性很高，这在从原始属性和较低维度嵌入空间中估计分子的原子数量的模型中得到了体现。