Big data and complex systems: towards a topological field theory of data

This talk aims to somehow challenge the current thinking in IT apropos of the methods to address the hard questions issuing from ‘Big Data’. Complexity Science and Data Science are at the root of the approach pursued. In the talk, an ongoing program is described that aims to construct an innovative methodology to perform data analytics in a way that may overcome the traditional Machine Learning data mining techniques, going beyond the well established theory of Complex Networks through the adoption of global (vs. local) topological approach to data sets. The method returns an automaton as recognizer of the data language: a Topological Field Theory of Data. A theoretical framework is built, directly out of probing data space, enabling us to extract the manifold hidden relations (patterns) that exist among information encoding data, as data field correlations depending on the semantics generated by the mining context. The program, grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a self-consistent Topological Field Theory of Data transferring and generalizing to the space of data notions inspired by physical (topological) statistical field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns. An example of successful application to medical data (fMRI for the brain) is briefly discussed.