vnsgm.ordered: Vertex Nomination via Seeded Graph Matching
In neurodata/graphstats: Graph Statistics

Description Usage Arguments Value Author(s) References

Finds the seeds in an h-hop induced nbd of G_1 around the VOI, x,that is, finds induced subgraph generated by vertices that are within a path of length h the VOI, and then finds an ell-hop induced nbd of G_1 around the seeds within the h-hop nbd of x, and an ell-hop induced nbd of G_2 around the corresponding seeds. Then, matches these induced subgraphs via multiStart. Assume first s vertices in two graphs are matched seeds.

1 2	vnsgm.ordered(x, s, g1, g2, h, ell, R, gamma, maxiter = 20, pad = 0, verbose = FALSE, plotF = FALSE)

`x`	vector of indices for vertices of interest (voi) in G_1
`s`	the number of seeds.
`g1`	G_1 in `igraph` object where voi is known
`g2`	G_2 in `igraph`
`h`	h-hop for distance from voi to other vertices to create h-hop induced subgraph of G_1
`ell`	ell-hop for distance from seeds to other vertices to create ell-hop induced subgraph of G_1
`R`	number of restarts for `multiStart`
`gamma`	to be used with `multiStart`, max tolerance for alpha, how far away from the barycenter user is willing to go for the initialization of `sgm` on any given iteration
`maxiter`	the number of maxiters for the Frank-Wolfe algorithm.
`pad`	a scalar value for padding for sgm (cases where two graphs have different number of vertices); defaulted to 0
`verbose`	logical verbose outputs
`plotF`	boolean to plot the probability matrix

VOI Vertex of Interest

seeds s seeds

Sx1 S_x the seeds within an h-path, i.e. in the h-neighborhood, of VOI x in G_1

Sx2 S'_x the corresponding seeds of S_x in G_2

candidates_for_matching labels for the candidates for matching VOIs in G_2

G1_vertices vertices within ell-neighborhood of S_x in G_1 (vertices used in vertex nomination for VOIs)

G2_vertices vertices within ell-neighborhood of S'_x in G_2 (including candidates x' for matching VOIs x in G_1)

P matrix P(i,j) is the proportion of times that vertex j in the induced subgraph of G_2 was mapped to vertex i in the induced subgraph of G_1. Then the i-th and j-th elements of the labels vector tells you which vertices these actually were in G_1 and G_2, respectively.

Youngser Park youngser@jhu.edu, Kemeng Zhang kzhang@jhu.edu

Patsolic, Heather G.; Park, Youngser; Lyzinski, Vince; Priebe, Carey E. (2017). Vertex Nomination Via Local Neighborhood Matching Online: https://arxiv.org/abs/1705.00674

Fishkind, D. E., Adali, S., Priebe, C. E. (2012). Seeded Graph Matching Online: http://arxiv.org/abs/1209.0367

neurodata/graphstats documentation built on May 14, 2019, 5:19 p.m.