Spectral Embedding of Adjacency Matrices
Spectral decomposition of the adjacency matrices of graphs.
embed_adjacency_matrix(
graph,
no,
weights = NULL,
which = c("lm", "la", "sa"),
scaled = TRUE,
cvec = graph.strength(graph, weights = weights)/(vcount(graph) - 1),
options = igraph.arpack.default
)graph |
The input graph, directed or undirected. |
no |
An integer scalar. This value is the embedding dimension of the
spectral embedding. Should be smaller than the number of vertices. The
largest |
weights |
Optional positive weight vector for calculating a weighted
embedding. If the graph has a |
which |
Which eigenvalues (or singular values, for directed graphs) to use. ‘lm’ means the ones with the largest magnitude, ‘la’ is the ones (algebraic) largest, and ‘sa’ is the (algebraic) smallest eigenvalues. The default is ‘lm’. Note that for directed graphs ‘la’ and ‘lm’ are the equivalent, because the singular values are used for the ordering. |
scaled |
Logical scalar, if |
cvec |
A numeric vector, its length is the number vertices in the graph. This vector is added to the diagonal of the adjacency matrix. |
options |
A named list containing the parameters for the SVD
computation algorithm in ARPACK. By default, the list of values is assigned
the values given by |
This function computes a no-dimensional Euclidean representation of
the graph based on its adjacency matrix, A. This representation is
computed via the singular value decomposition of the adjacency matrix,
A=UDV^T.In the case, where the graph is a random dot product graph
generated using latent position vectors in R^{no} for each vertex, the
embedding will provide an estimate of these latent vectors.
For undirected graphs the latent positions are calculated as
U[no] sqrt(D[no]), where U[no] equals
to the first no columns of U, and sqrt(D[no]) is
a diagonal matrix containing the top no singular values on the
diagonal.
For directed graphs the embedding is defined as the pair U[no] sqrt(D[no]) and V[no] sqrt(D[no]). (For undirected graphs U=V, so it is enough to keep one of them.)
A list containing with entries:
X |
Estimated latent positions,
an |
Y |
|
D |
The eigenvalues (for undirected graphs) or the singular values (for directed graphs) calculated by the algorithm. |
options |
A named list, information about the underlying ARPACK
computation. See |
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
## 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_adjacency_matrix(RDP, 5)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.