Structure-property maps with Kernel principal covariates regression

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.

Origins of structural and electronic transitions in disordered silicon

“…Finally, by combining the structural information (from SOAP similarity, as used in Fig. 2g) and the machine-learned electronic fingerprints, we may construct structure-property maps for atomic environments using kernel principal covariates regression 47 . This approach yields 2D slices that map out the atomic environments, arranged so as to reflect structural diversity and also the relationship between structure and metallicity, for which the locally-averaged ML DOS(EF) is used as a proxy 42 .…”

“…To this end, we use the recently-introduced kernel principal covariates regression (KPCovR) method, described in Ref. 47, that can be seen as a modified kernel principal-component analysis in which one uses a modified kernel with a scaling parameter, ,…”

“…In all plots, EF is set as the energy zero. (e) Evolution of the atomic environments during our compression simulation, visualised using kernel principal covariates regression (KPCovR)47 . The axes (components) provide the 2D projection of the SOAP kernel 32 features that gives the best balance between discriminating the structural diversity of the environments, and linearly predicting the locally-averaged ML DOS(EF).…”

Reaction-based machine learning representations for predicting the enantioselectivity of organocatalysts

“…Similarly, methods based on metric learning 111,115 did not lead to any improvement, as the high dimensionality of the problem led to severe overtting. Ceriotti et al 116 suggested the use of principal covariates regression (PCovR) to solve similar issues. 117 PCovR is a supervised feature selection method that interpolates between principal component analysis (PCA) and linear regression.…”

“…Ceriotti et al 116 suggested the use of principal covariates regression (PCovR) to solve similar issues. 117 PCovR is a supervised feature selection method that interpolates between principal component analysis (PCA) and linear regression. Herein, because the variance of the features is completely unrelated to the importance scores, the addition of PCA would not offer any advantage.…”