We first investigated dimensionality reduction using PCA of the ACSFs and the SOAP kernel. In both cases, the descriptors were flattened over all atoms and, for symmetry functions, radial and angular functions were merged into one vector. With either descriptor, the eigenvalues corresponding to the first two principle components had twice the magnitude of the third. We plot the structures onto these first two principal components in Figure (see ESI for the corresponding plot for ACSFs, Fig. ). In neither case is there clear differentiation of structures corresponding to basins I and II, as identified by the threshold algorithm; the structures from both basins, and those outside of the two basins, overlap in this projection onto the first two principal components.