  We introduce an unsupervised clustering algorithm to improve training
efficiency and accuracy in predicting energies using molecular-orbital-based
machine learning (MOB-ML). This work determines clusters via the Gaussian
mixture model (GMM) in an entirely automatic manner and simplifies an earlier
supervised clustering approach [J. Chem. Theory Comput., 15, 6668 (2019)] by
eliminating both the necessity for user-specified parameters and the training
of an additional classifier. Unsupervised clustering results from GMM have the
advantage of accurately reproducing chemically intuitive groupings of frontier
molecular orbitals and having improved performance with an increasing number of
training examples. The resulting clusters from supervised or unsupervised
clustering is further combined with scalable Gaussian process regression (GPR)
or linear regression (LR) to learn molecular energies accurately by generating
a local regression model in each cluster. Among all four combinations of
regressors and clustering methods, GMM combined with scalable exact Gaussian
process regression (GMM/GPR) is the most efficient training protocol for
MOB-ML. The numerical tests of molecular energy learning on thermalized
datasets of drug-like molecules demonstrate the improved accuracy,
transferability, and learning efficiency of GMM/GPR over not only other
training protocols for MOB-ML, i.e., supervised regression-clustering combined
with GPR(RC/GPR) and GPR without clustering. GMM/GPR also provide the best
molecular energy predictions compared with the ones from literature on the same
benchmark datasets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in
wall-clock training time compared with scalable exact GPR with a training size
of 6500 QM7b-T molecules.
