LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential. We introduce a novel class of localized atomic environment representations based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biomolecular datasets demonstrate that potentials created with LC-GAP can successfully predict atomization energies for molecules larger than those used for training to chemical accuracy, and can (in the case of QM7b) also be used to predict a range of other atomic properties with accuracy in line with the recent literature. As the best-performing representation has only linear dimensionality in the number of atoms in a local atomic environment, this represents an improvement in both prediction accuracy and computational cost when compared to similar Coulomb matrix-based methods.