Exploring the shape of data for discovering patterns in crystal chemistry

This paper describes an unsupervised exploratory data mining strategy for identifying significant chemistry-structure–property relationships in complex crystal chemistries. Using the formalism of Topological Data Analysis (TDA), we show how hierarchical patterns in families of crystal structures of the apatite family of the type A1₅A2₅B1B2O₂₄X can be automatically detected via TDA. This ‘self-driving’ data exploration approach is shown not only to uncover links between structural building units and different stoichiometries but also to uncover new and yet unexplored associations between properties and coordination polyhedral geometry. Graphic abstract: [Figure not available: see fulltext.].