AABBA Graph Kernel: Atom-Atom, Bond-Bond, and Bond-Atom Autocorrelations for Machine Learning

Graphs are one of the most natural and powerful representations available for molecules; natural because they have an intuitive correspondence to skeletal formulas, the language used by chemists worldwide, and powerful, because they are highly expressive both globally (molecular topology) and locally (atom and bond properties). Graph kernels are used to transform molecular graphs into fixed-length vectors, which, based on their capacity of measuring similarity, can be used as fingerprints for machine learning (ML). To date, graph kernels have mostly focused on the atomic nodes of the graph. In this work, we developed a graph kernel based on atom-atom, bond-bond, and bond-atom (AABBA) autocorrelations. The resulting vector representations were tested on regression ML tasks on a data set of transition metal complexes; a benchmark motivated by the higher complexity of these compounds relative to organic molecules. In particular, we tested different flavors of the AABBA kernel in the prediction of the energy barriers and bond distances of the Vaska's complex data set (Friederich et al., Chem. Sci., 2020, 11, 4584). For a variety of ML models, including neural networks, gradient boosting machines, and Gaussian processes, we showed that AABBA outperforms the baseline including only atom-atom autocorrelations. Dimensionality reduction studies also showed that the bond-bond and bond-atom autocorrelations yield many of the most relevant features. We believe that the AABBA graph kernel can accelerate the exploration of large chemical spaces and inspire novel molecular representations in which both atomic and bond properties play an important role.