An undirected factor model graph is an undirected
generalized Poisson random dot product graph. The edges
in this graph are assumed to be independent and Poisson
distributed. The graph is parameterized by its expected
adjacency matrix, which is E[A|X] = X S X'. We do not recommend
that casual users use this function, see instead dcsbm()
and related functions, which will formulate common variants
of the stochastic blockmodels as undirected factor models
with lots of helpful input validation.
undirected_factor_model(
X,
S,
...,
expected_degree = NULL,
expected_density = NULL,
poisson_edges = TRUE,
allow_self_loops = TRUE
)An undirected_factor_model S3 class based on a list
with the following elements:
X: The latent positions as a Matrix() object.
S: The mixing matrix as a Matrix() object.
n: The number of nodes in the network.
k: The rank of expectation matrix. Equivalently,
the dimension of the latent node position vectors.
A matrix() or Matrix() representing real-valued
latent node positions. Entries must be positive.
A matrix() or Matrix() mixing matrix. S is
symmetrized if it is not already, as this is the undirected
case. Entries must be positive.
Ignored. Must be empty.
If specified, the desired expected degree
of the graph. Specifying expected_degree simply rescales S
to achieve this. Defaults to NULL. Do not specify both
expected_degree and expected_density at the same time.
If specified, the desired expected density
of the graph. Specifying expected_density simply rescales S
to achieve this. Defaults to NULL. Do not specify both
expected_degree and expected_density at the same time.
Logical indicating whether or not
multiple edges are allowed to form between a pair of
nodes. Defaults to TRUE. When FALSE, sampling proceeds
as usual, and duplicate edges are removed afterwards. Further,
when FALSE, we assume that S specifies a desired between-factor
connection probability, and back-transform this S to the
appropriate Poisson intensity parameter to approximate Bernoulli
factor connection probabilities. See Section 2.3 of Rohe et al. (2017)
for some additional details.
Logical indicating whether or not
nodes should be allowed to form edges with themselves.
Defaults to TRUE. When FALSE, sampling proceeds allowing
self-loops, and these are then removed after the fact.
n <- 10000
k <- 5
X <- matrix(rpois(n = n * k, 1), nrow = n)
S <- matrix(runif(n = k * k, 0, .1), nrow = k)
ufm <- undirected_factor_model(X, S)
ufm
ufm2 <- undirected_factor_model(X, S, expected_degree = 50)
ufm2
svds(ufm2)
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