Knowledge mining in big data — A lesson from algebraic geometry

Author

Jun Xie ; Zehua Chen ; Gang Xie ; Lin, Tsau Young

Author_Institution

Coll. of Inf. Eng., Taiyuan Univ. of Technol., Taiyuan, China

fYear

2013

fDate

13-15 Dec. 2013

Firstpage

362

Lastpage

367

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”.

Keywords

algebra; data handling; data mining; geometry; granular computing; set theory; topology; GrC framework; Zariski topology; algebraic geometry; big data; granular computing approach; granular structure; hidden geometric structure computation; knowledge mining; knowledge structure; mathematical framework; prime ideal set selection; quotient structure; Computational modeling; Data handling; Data storage systems; Geometry; Information management; Mathematical model; Topology; Spectrum; Zariski Topology; algebraic geometry; central knowledge; derived partition; granular computing; granular structure; knowledge structure; neighborhood system; quotient structure;

fLanguage

English

Publisher

ieee

Conference_Titel

Granular Computing (GrC), 2013 IEEE International Conference on

Conference_Location

Beijing

Type

conf

DOI

10.1109/GrC.2013.6740437

Filename

6740437