LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

MVTree for Hierarchical Network Representation Based on Geometric Algebra Subspace

Photo from wikipedia

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… Click to show full 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: network; based geometric; network representation; hierarchical network; subspace; representation

Journal Title: Advances in Applied Clifford Algebras
Year Published: 2018

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.