Abstract
Data analyses based on linear methods constitute the simplest, most robust, and transparent approaches to the automatic processing of large amounts of data for building supervised or unsupervised machine learning models. Principal covariates regression (PCovR) is an underappreciated method that interpolates between principal component analysis and linear regression and can be used conveniently to reveal structure-property relations in terms of simple-to-interpret, low-dimensional maps. Here we provide a pedagogic overview of these data analysis schemes, including the use of the kernel trick to introduce an element of non-linearity while maintaining most of the convenience and the simplicity of linear approaches. We then introduce a kernelized version of PCovR and a sparsified extension, and demonstrate the performance of this approach in revealing and predicting structure-property relations in chemistry and materials science, showing a variety of examples including elemental carbon, porous silicate frameworks, organic molecules, amino acid conformers, and molecular materials.
Highlights
Over the past decade, there has been a tremendous increase in the use of data-driven and machine learning (ML) methods in materials science, ranging from the prediction of materials properties [1,2,3,4], to the construction of interatomic potentials [5,6,7,8] and searches for new candidate materials for a particular application [9,10,11,12]
In this paper we provide a comprehensive overview of linear- and kernel-based methods for supervised and unsupervised learning, showing an example of their application to elucidate and predict structure-property relations in solid-state NMR
We discuss a simple combination of principal component analysis and linear regression, Principal covariates regression (PCovR) [18], that has as yet received far less attention than in our opinion it deserves
Summary
Keywords: machine learning, structure-property maps, kernel methods, materials science, physical chemistry Supplementary material for this article is available online Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.
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