Dynamic geometric graph processes: adjacency operator approach

René Schott (1, 2) , Stacey Staples (3)

1 IECN - Institut Élie Cartan de Nancy
2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 Department of Mathematics and Statistics - Southern Illinois University

The $d$-dimensional unit cube $[0; 1]^d$ is discretized to create a collection $V$ of vertices used to dene geometric graphs. Each subset of $V$ is uniquely associated with a geometric graph. Dening a dynamic random walk on the subsets of $V$ induces a walk on the collection of geometric graphs in the discretized cube. These walks naturally model addition-deletion networks and can be visualized as walks on hypercubes with loops. Adjacency operators are constructed using subalgebras of Cliord algebras and are used to recover information about the cycle structure and connected components of the $n$ graph of a sequence.

Domaines: Probabilités [math.PR]

René Schott, Stacey Staples. Dynamic geometric graph processes: adjacency operator approach. Advances in Applied Clifford Algebras, 2010, 20 (3-4), pp.893-921. ⟨10.1007/s00006-010-0228-6⟩. ⟨hal-00438175⟩