# Measuring the Similarity between Materials with an Emphasis on the Materials Distinctiveness

## TL;DR

This paper investigates how selecting similarity measures that preserve materials' distinctiveness enhances machine learning predictions in materials science, using case studies with various descriptors and regression methods.

## Contribution

It provides a framework for choosing similarity measures that maintain material distinctiveness, improving prediction accuracy in materials property modeling.

## Key findings

- Similarity measures that preserve material distinctiveness improve prediction accuracy.
- Kernel methods that minimize loss of distinctiveness perform better.
- Analysis links descriptor characteristics with similarity measure effectiveness.

## Abstract

In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that reflect their nature well. We perform a case study with a dataset of rare-earth transition metal crystalline compounds represented using the Orbital Field Matrix descriptor and the Coulomb Matrix descriptor. We perform predictions of the formation energies using k-nearest neighbors regression, ridge regression, and kernel ridge regression. Through detailed analyses of the yield prediction accuracy, we examine the relationship between the characteristics of the material representation and similarity measures, and the complexity of the energy function they can capture. Empirical experiments and theoretical analysis reveal that similarity measures and kernels that minimize the loss of materials distinctiveness improve the prediction performance.