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.

基于线性方法的数据分析构成了用于构建监督或无监督机器学习模型的自动处理大量数据的最简单，最可靠和透明的方法。主协变量回归（PCovR）是一种在主成分分析和线性回归之间进行插值的方法，其被低估了，可以方便地用于以易于解释的低维图显示结构与属性的关系。在这里，我们提供了有关这些数据分析方案的教学概述，包括使用内核技巧介绍非线性元素，同时保留了线性方法的大多数便利性和简便性。然后，我们介绍PCovR的内核版本和稀疏的扩展，