MVTree for Hierarchical Network Representation Based on Geometric Algebra Subspace

  • Shuai Zhu
  • Shuai Yuan
  • Dongshuang Li
  • Wen Luo
  • Linwang Yuan
  • Zhaoyuan Yu
Article
  • 32 Downloads
Part of the following topical collections:
  1. T.C. : Geometric Algebra for Computing, Graphics and Engineering with Yu Zhaoyuan, Guest E-i-C

Abstract

Most hierarchical representation methods are designed from engineering perspectives, lacking an appropriate mathematical foundation to integrate different problem definitions. To solve this problem, a hierarchical network representation model based on geometric algebra (GA) subspace is proposed. In this paper, we give a new definition of hierarchical network representation, in which the network nodes are divided into several independent components and multi-level network is constructed based on it. Then these network nodes are coded with basis vectors and the subspace in GA is utilized to represent these nodes of component. Within a subspace or between different subspaces, the topological relation between different basis vectors is defined to connect different subspaces and the complete multi-level network can be formed according to these topological relations in subspaces of different level. A case study is used to show how GA is used to realize the hierarchical network representation and the result indicates that GA can provide an appropriate mathematical foundation for hierarchical network representation.

Keywords

Hierarchical network Geometric algebra subspace Topological relation Upper network 

Mathematics Subject Classification

Primary 99Z99 Secondary 00A00 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Shuai Zhu
    • 1
  • Shuai Yuan
    • 1
  • Dongshuang Li
    • 1
  • Wen Luo
    • 1
  • Linwang Yuan
    • 1
  • Zhaoyuan Yu
    • 1
  1. 1.Geography Department of Nanjing Normal UniversityXianLin School of Nanjing Normal UniversityNanjing CityChina

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