B0708
Title: Topological data analysis meets design of experiments: An exploration of 2-level non-isomorphic orthogonal arrays
Authors: Roberto Fontana - Politecnico di Torino (Italy) [presenting]
Marco Guerra - Politecnico di Torino (Italy)
Abstract: Orthogonal arrays (OAs) are a key topic within the field of design of experiments. A 2-level orthogonal array is observed with d factors corresponding to a unique d-variate Bernoulli distribution. A novel construction is proposed that associates to any d-variate Bernoulli probability mass function a filtered, abstract simplicial complex of dimension d, in such a way that this association is bijective. A filtered complex gives rise to a persistence module, the main object in topological data analysis (TDA). This, in turn, allows one to employ the tools of TDA in the field of orthogonal arrays. It explores how isomorphisms of OAs interact with the topological description, and, in particular, it is observed how a well-known notion of distance between persistence modules, the Wasserstein distance, appears to cluster OAs according to their isomorphism class. A Python implementation of the proposed construction and all experiments is provided.
