gaussian_snapshot_ss {fase} | R Documentation |
Simulate Gaussian edge networks with nonparametric latent processes
Description
gaussian_snapshot_ss
simulates a realization of a functional network
with Gaussian edges, according to an inner product latent process model.
The latent processes are randomly generated sinusoidal functions.
Usage
gaussian_snapshot_ss(n,d,m,x_vec,self_loops=TRUE,
sigma_edge=1,process_options)
Arguments
n |
A positive integer, the number of nodes. |
d |
A positive integer, the number of latent space dimensions. |
m |
A positive integer, the number of snapshots.
If this argument is not specified, it
is determined from the snapshot index vector |
x_vec |
A vector, the snapshot evaluation indices for the data.
Defaults to an equally spaced sequence of length
|
self_loops |
A Boolean, if |
sigma_edge |
A positive scalar,
the entry-wise standard deviation for the Gaussian edge variables.
Defaults to |
process_options |
A list, containing additional optional arguments:
|
Details
The the latent process for node in latent dimension
is given independently by
Where is Gaussian with mean
0
and standard deviation
,
is Bernoulli with mean
1/2
, and is uniform
with minimum
spline_design$x_min
and maximum spline_design$x_max
.
is a frequency parameter specified with
process_options$frequency
, and is a maximum amplitude parameter
specified with
process_options$amplitude
.
Roughly, each process is a randomly shifted sine function which goes through
f
cycles on the index set, with amplitude either increasing or
decreasing between and
.
Then, the symmetric adjacency matrix for
snapshot
has independent Gaussian entries
with standard deviation
sigma_edge
and mean
for (or
with no self loops).
This function may return the latent processes as an
array evaluated at the prespecified snapshot indices, or as a function which
takes a vector of indices and returns the corresponding evaluations of
the latent process matrices.
It also returns the spline design information required to
fit a FASE embedding to this data with a natural cubic spline.
Value
A list is returned with the realizations of the basis coordinates, spline design, and the multiplex network snapshots:
A |
An array of dimension |
Z |
If |
spline_design |
A list, describing the
|
Examples
# Gaussian edge data with sinusoidal latent processes
# NOTE: latent processes are returned as a function
data <- gaussian_snapshot_ss(n=100,d=2,
x_vec=seq(0,3,length.out=80),
self_loops=TRUE,
sigma_edge=4,
process_options=list(amplitude=4,
frequency=3,
return_fn=TRUE))