def sample_hw_graph(thetas):
latent = hardy_weinberg(thetas)
p_mat = p_from_latent(latent, rescale=False, loops=False)
graph = sample_edges(p_mat, directed=False, loops=False)
return (graph, p_mat, latent)
def gen_hw_graph(n_verts):
thetas = np.random.uniform(0, 1, n_verts)
latent = hardy_weinberg(thetas)
p_mat = p_from_latent(latent, rescale=False, loops=False)
graph = sample_edges(p_mat, directed=True, loops=False)
return (graph, p_mat)
def rdpg_corr(X, Y, r, rescale=False, directed=False, loops=False):
r"""
Samples a random graph pair based on the latent positions in X (and
optionally in Y)
If only X :math:`\in\mathbb{R}^{n\times d}` is given, the P matrix is calculated as
:math:`P = XX^T`. If X, Y :math:`\in\mathbb{R}^{n\times d}` is given, then
:math:`P = XY^T`. These operations correspond to the dot products between a set of
latent positions, so each row in X or Y represents the latent positions in
:math:`\mathbb{R}^{d}` for a single vertex in the random graph
Note that this function may also rescale or clip the resulting P
matrix to get probabilities between 0 and 1, or remove loops.
A binary random graph is then sampled from the P matrix described
by X (and possibly Y).
Read more in the :ref:`tutorials <simulations_tutorials>`
Parameters
----------
X: np.ndarray, shape (n_vertices, n_dimensions)
latent position from which to generate a P matrix
if Y is given, interpreted as the left latent position
Y: np.ndarray, shape (n_vertices, n_dimensions) or None, optional
right latent position from which to generate a P matrix
r: float
The value of the correlation between the same vertices in two graphs.
rescale: boolean, optional (default=True)
when rescale is True, will subtract the minimum value in
P (if it is below 0) and divide by the maximum (if it is
above 1) to ensure that P has entries between 0 and 1. If
False, elements of P outside of [0, 1] will be clipped.
directed: boolean, optional (default=False)
If False, output adjacency matrix will be symmetric. Otherwise, output adjacency
matrix will be asymmetric.
loops: boolean, optional (default=True)
If False, no edges will be sampled in the diagonal. Diagonal elements in P
matrix are removed prior to rescaling (see above) which may affect behavior.
Otherwise, edges are sampled in the diagonal.
Returns
-------
G1: ndarray (n_vertices, n_vertices)
A matrix representing the probabilities of connections between
vertices in a random graph based on their latent positions
G2: ndarray (n_vertices, n_vertices)
A matrix representing the probabilities of connections between
vertices in a random graph based on their latent positions
References
----------
.. [1] Vince Lyzinski, Donniell E Fishkind profile imageDonniell E. Fishkind, Carey E Priebe.
"Seeded graph matching for correlated Erdös-Rényi graphs".
The Journal of Machine Learning Research, January 2014
Examples
--------
>>> np.random.seed(1234)
>>> X = np.random.dirichlet([1, 1], size=5)
>>> Y = None
Generate random latent positions using 2-dimensional Dirichlet distribution.
Then sample a correlated RDPG graph pair:
>>> rdpg_corr(X, Y, 0.3, rescale=False, directed=False, loops=False)
(array([[0., 1., 0., 1., 0.],
[1., 0., 0., 1., 1.],
[0., 0., 0., 0., 0.],
[1., 1., 0., 0., 0.],
[0., 1., 0., 0., 0.]]), array([[0., 1., 0., 1., 0.],
[1., 0., 0., 0., 1.],
[0., 0., 0., 0., 0.],
[1., 0., 0., 0., 0.],
[0., 1., 0., 0., 0.]]))
"""
# check r
if not np.issubdtype(type(r), np.floating):
raise TypeError("r is not of type float.")
elif r < -1 or r > 1:
msg = "r must between -1 and 1."
raise ValueError(msg)
# check directed and loops
if type(directed) is not bool:
raise TypeError("directed is not of type bool.")
if type(loops) is not bool:
raise TypeError("loops is not of type bool.")
# check dimensions of X and Y
if Y != None:
if type(X) is not np.ndarray or type(Y) is not np.ndarray:
raise TypeError("Latent positions must be numpy.ndarray")
if X.ndim != 2 or Y.ndim != 2:
raise ValueError(
"Latent positions must have dimension 2 (n_vertices, n_dimensions)"
)
if X.shape != Y.shape:
raise ValueError("Dimensions of latent positions X and Y must be the same")
if Y is None:
Y = X
P = p_from_latent(X, Y, rescale=rescale, loops=loops)
n = P.shape[0]
R = np.full((n, n), r)
G1, G2 = sample_edges_corr(P, R, directed=directed, loops=loops)
return G1, G2
#%%
import numpy as np
import seaborn as sns
from graspy.inference import LatentDistributionTest
from graspy.simulations import p_from_latent, sample_edges
from tqdm import tqdm
n_sims = 200
n_verts = 200
n_components = 2
latent_size = (n_verts, n_components)
directed = False
latent = np.random.uniform(0.2, 0.5, size=latent_size)
p_mat = p_from_latent(latent, rescale=False, loops=False)
sim_p_vals = np.zeros(n_sims)
for i in tqdm(range(n_sims)):
graph1 = sample_edges(p_mat, directed=directed, loops=False)
graph2 = sample_edges(p_mat, directed=directed, loops=False)
ldt = LatentDistributionTest(n_components=n_components, n_bootstraps=1000)
out = ldt.fit(graph1, graph2)
p_val = ldt.p_
sim_p_vals[i] = p_val
#%%
from graspy.plot import pairplot
pairplot(latent)
from graspy.embed import AdjacencySpectralEmbed