AABBA Graph Kernel:\nAtom-Atom, Bond-Bond, and Bond-Atom\nAutocorrelations for Machine Learning

Graphs are one of the most natural and powerful representations\navailable for molecules; natural because they have an intuitive correspondence\nto skeletal formulas, the language used by chemists worldwide, and\npowerful, because they are highly expressive both globally (molecular\ntopology) and locally (atom and bond properties). Graph kernels are\nused to transform molecular graphs into fixed-length vectors, which,\nbased on their capacity of measuring similarity, can be used as fingerprints\nfor machine learning (ML). To date, graph kernels have mostly focused\non the atomic nodes of the graph. In this work, we developed a graph\nkernel based on atom-atom, bond-bond, and bond-atom (AABBA) autocorrelations.\nThe resulting vector representations were tested on regression ML\ntasks on a data set of transition metal complexes; a benchmark motivated\nby the higher complexity of these compounds relative to organic molecules.\nIn particular, we tested different flavors of the AABBA kernel in\nthe prediction of the energy barriers and bond distances of the Vaska’s\ncomplex data set (Friederich et al., <i>Chem. Sci.</i>,\n2020, <b>11,</b> 4584). For a variety of ML models, including\nneural networks, gradient boosting machines, and Gaussian processes,\nwe showed that AABBA outperforms the baseline including only atom-atom\nautocorrelations. Dimensionality reduction studies also showed that\nthe bond-bond and bond-atom autocorrelations yield many of the most\nrelevant features. We believe that the AABBA graph kernel can accelerate\nthe exploration of large chemical spaces and inspire novel molecular\nrepresentations in which both atomic and bond properties play an important\nrole.