# Structure-Property Maps with Kernel Principal Covariates Regression

arXiv: https://arxiv.org/abs/2002.05076 · HTML: https://mlsanity.com/paper/2002.05076/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [Optimal radial basis for density-based atomic representations](https://mlsanity.com/paper/2105.08717/) (2021)
- [Synthetic data enable experiments in atomistic machine learning](https://mlsanity.com/paper/2211.16443/) (2022)
- [Interpretable Visualizations of Data Spaces for Classification Problems](https://mlsanity.com/paper/2503.05861/) (2025)
- [Machine Learning Workflow for Analysis of High-Dimensional Order Parameter Space: A Case Study of Polymer Crystallization from Molecular Dynamics Simulations](https://mlsanity.com/paper/2507.17980/) (2025)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

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 to conveniently 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.