Understanding the Structure of QM7b and QM9 Quantum Mechanical Datasets
  Using Unsupervised Learning
Julio J. Valdés Alain B. Tchagang
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.