  We show how to speed up global optimization of molecular structures using
machine learning methods. To represent the molecular structures we introduce
the auto-bag feature vector that combines: i) a local feature vector for each
atom, ii) an unsupervised clustering of such feature vectors for many atoms
across several structures, and iii) a count for a given structure of how many
times each cluster is represented. During subsequent global optimization
searches, accumulated structure-energy relations of relaxed structural
candidates are used to assign local energies to each atom using supervised
learning. Specifically, the local energies follow from assigning energies to
each cluster of local feature vectors and demanding the sum of local energies
to amount to the structural energies in the least squares sense. The usefulness
of the method is demonstrated in basin hopping searches for 19-atom structures
described by single- or double-well Lennard- Jones type potentials and for
24-atom carbon structures described by density functional theory (DFT). In all
cases, utilizing the local energy information derived on-the-fly enhances the
rate at which the global minimum energy structure is found.
