gs.embed.lse: Spectral Embedding of the Laplacian of a Graph

In neurodata/graphstats: Graph Statistics

Description

Spectral decomposition of Laplacian matrices of graphs.

Usage

gs.embed.lse(g, k = NULL, edge.attr = NULL)

Arguments

g	an igraph object or an nxn adjacency matrix with n vertices.
edge.attr	if g is a igraph, the name of the attribute to use for weights. Defaults to NULL, which assumes the graph is binary. is.null(edge.attr) assumes unweighted. is.character(edge.attr) assumes weighted with weights given by edge.attr.

Details

This function computes a k-dimensional Euclidean representation of the graph based on its Laplacian matrix, L. This representation is computed via the singular value decomposition of the Laplacian matrix.

Value

A list containing the following:

X	an n by k matrix indicating the estimated latent positions, where n is the number of vertices of g.
Y	NULL if g is undirected. If g is directed, Y is a n by k matrix indicating the second half of the latent positions.
D	The eigenvalues (for undirected graphs) or the singular values (for directed graphs) associated with the latent positions.

Author(s)

Eric Bridgeford [e-mail]

References

Sussman, D.L., Tang, M., Fishkind, D.E., Priebe, C.E. A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs, Journal of the American Statistical Association, Vol. 107(499), 2012

Examples

## A small graph
lpvs <- matrix(rnorm(200), 20, 10)
lpvs <- apply(lpvs, 2, function(x) { return (abs(x)/sqrt(sum(x^2))) })
RDP <- sample_dot_product(lpvs)
embed <- embed_laplacian_matrix(RDP, 5)
TODO ebridge2

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