Given the high dimensionality of the SOAP vectors we use dimensionality reduction to simplify the interpretation of the results. The use of these algorithms has become commonplace in computational science and has proven to provide a great qualitative understanding of complex structures in different type of materials. These algorithms seek to find an optimal low-dimensional embedding capable of capturing the shape of a high-dimensional manifold, which would be impossible to visualize otherwise. PCA is probably the simplest statistical algorithm among all the dimensionality reduction schemes, yet it performed very well once combined with PAMM clustering in projecting in lowdimensions all the different high-dimensional motifs. The PCA linearly transforms a set of correlated data into a new set of values of variables linearly uncorrelated, called principal components. All the two dimensional maps discussed in the text were obtained using the PCA implementation available in SciKit-Learn, by projecting points from the high-dimensional SOAP feature space to two dimensions using the first two principal components. Two dimensions are clearly not enough to capture all the complexity of the initial manifold, however for our systems this is already quite informative since the first two principal components alone explain ∼74% of the full covariance (see SI for further details).