# Understanding the Structure of QM7b and QM9 Quantum Mechanical Datasets Using Unsupervised Learning

arXiv: https://arxiv.org/abs/2309.15130 · HTML: https://mlsanity.com/paper/2309.15130/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 25 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Application of generative autoencoder in de novo molecular design](https://mlsanity.com/paper/1711.07839/) (2017)
- [LSCP: Locally Selective Combination in Parallel Outlier Ensembles](https://mlsanity.com/paper/1812.01528/) (2018)
- [Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations](https://mlsanity.com/paper/1902.05804/) (2019)
- [Intrinsic Dimensionality Estimation within Tight Localities: A Theoretical and Experimental Analysis](https://mlsanity.com/paper/2209.14475/) (2022)
- [Estimating the effective dimension of large biological datasets using Fisher separability analysis](https://mlsanity.com/paper/1901.06328/) (2019)
- [Correction of AI systems by linear discriminants: Probabilistic foundations](https://mlsanity.com/paper/1811.05321/) (2018)
- [Tree-SNE: Hierarchical Clustering and Visualization Using t-SNE](https://mlsanity.com/paper/2002.05687/) (2020)

## Built on by (most cited first, 1 of 1)

- [Evolutionary-enhanced quantum supervised learning model](https://mlsanity.com/paper/2311.08081/) (2023)

## Abstract (arXiv)

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.