ABSTRACT
This chapter discusses some mathematical approaches based on the topological properties of data, and a specific application to the automated extraction of Bayesian networks from textual sources. The evaluation results show the potential of this approach, which in turn could be applied to a wider range of topics to advance the understanding of data science and its applications. Research in big data has been the focus of numerous research communities, resulting in the advance of novel theories and applications to address the crucial challenges arising from the Four Vs, namely, volume, velocity, variety, and veracity. Topology aims to understand invariant properties of spaces, providing a global classification of spaces, as opposed to attempting to assess their local properties. This can provide a powerful approach to big data where a very fine granularity might prove counterproductive. Topological data analysis is an emerging research field, which aims to apply theoretical approaches in topology to data science.
