Knowledge mining in big data — A lesson from algebraic geometry

Abstract

A granular computing (GrC) approach of a mathematical framework for “knowledge mining in Big Data” is illustrated by using some idea from algebraic geometry: (1) For example, the ring of the integers, denoted by Z, is a model U of `Big Data' (the discourse of universe of `Big Data'). (2) The selection of the set of prime ideals is an example of granulating (MAPping) the “Big Data” U into granular structure. (3) To compute the hidden geometric structure of Spec(Z) (e.g., Zariski topology) is to compute (to REDUCE) the quotient structure and and to interpret into knowledge structure. The transformation of algebraic structure of Z to geometric structure of Spec(Z) is the GrC framework of “knowledge mining in Big Data”.