Non locality, Topology, Formal Languages: New Global Tools to Handle Large Data Sets

The basic idea that stems out of this work is that large sets of data can be handled through an organized set of mathematical and computational tools rooted in a global geometric vision of data space allowing to explore the structure and hidden information patterns thereof. Based on this perspective, the objective is naturally that of discovering and letting emerge, directly from probing the data space, the manifold hidden relations (patterns), e.g. correlations among facts, interactions among entities, relations among concepts and formally describing, in a semantic mining context, the discovered information. In this note, we propose an approach that exploits topological methods for classifying global information into equivalence classes and regular languages for describing the corresponding automaton as element an of hidden complex system.