sgm: Matches Graphs given a seeding of vertex correspondences
In youngser/VN: Vertex Nomination via Seeded Graph Matching

Description Usage Arguments Details Value Author(s) References

Given two adjacency matrices A and B of the same size, match the two graphs with the help of m seed vertex pairs which correspond to m rows (and columns) of the adjacency matrices.

1	sgm(A, B, seeds, hard = TRUE, pad = 0, start = "barycenter", maxiter = 20)

`A`	a numeric matrix, the adjacency matrix of the first graph
`B`	a numeric matrix, the adjacency matrix of the second graph
`seeds`	a numeric matrix, the number of seeds x 2 matching vertex table. If `S` is `NULL`, then it is using a soft seeding algorithm.
`hard`	a bloolean, TRUE for hard seeding, FALSE for soft seeding.
`pad`	a scalar value for padding
`maxiter`	The number of maxiters for the Frank-Wolfe algorithm

The approximate graph matching problem is to find a bijection between the vertices of two graphs , such that the number of edge disagreements between the corresponding vertex pairs is minimized. For seeded graph matching, part of the bijection that consist of known correspondences (the seeds) is known and the problem task is to complete the bijection by estimating the permutation matrix that permutes the rows and columns of the adjacency matrix of the second graph.

It is assumed that for the two supplied adjacency matrices A and B, both of size n*n, the first m rows(and columns) of A and B correspond to the same vertices in both graphs. That is, the n*n permutation matrix that defines the bijection is I_{m} \bigoplus P for a (n-m)*(n-m) permutation matrix P and m times m identity matrix I_{m}. The function match_vertices estimates the permutation matrix P via an optimization algorithm based on the Frank-Wolfe algorithm.

See references for further details.

A numeric matrix which is the permutation matrix that determines the bijection between the graphs of A and B

Vince Lyzinski http://www.ams.jhu.edu/~lyzinski/

Vogelstein, J. T., Conroy, J. M., Podrazik, L. J., Kratzer, S. G., Harley, E. T., Fishkind, D. E.,Vogelstein, R. J., Priebe, C. E. (2011). Fast Approximate Quadratic Programming for Large (Brain) Graph Matching. Online: http://arxiv.org/abs/1112.5507

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

youngser/VN documentation built on July 18, 2020, 12:48 p.m.