Topological Field Theory of Data: Mining Data Beyond Complex Networks

This paper aims to challenge the current thinking in IT for the Big Data question, proposing a program aiming to construct an innovative methodology to perform data analytics that goes beyond the usual paradigms of data mining rooted in the notions of Complex Networks and Machine Learning. The method developed – at least as scheme – that returns an automaton as a recognizer of the data language, is, to all effects, a Field Theory of Data. It is discussed how to build, directly out of probing the data space, a theoretical framework enabling us to extract the manifold hidden relations (patterns) that exist among data as correlations depending on the semantics generated by the mining context. The program, that is grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a Topological field theory of data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns.