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How to measure the complexity of a finite set of vectors embedded in a multidimensional space? This is a non-trivial question which can be approached in many different ways. Here we suggest a set of data complexity measures using universal approximators, principal cubic complexes. Principal cubic complexes generalise the notion of principal manifolds for datasets with non-trivial topologies. The type of the principal cubic complex is determined by its dimension and a grammar of elementary graphdoi:10.1016/j.camwa.2012.12.009 fatcat:p7zk33pt4rbc5nyupapc45h52i