def get(n=50):
ns = [n, n]
p1 = np.array([[.9,.1],[.1,.9]])
p2 = np.array([[.9,.1],[.1,.9]])
A1 = sbm(ns,p1)
A2 = sbm(ns,p2)
X1 = AdjacencySpectralEmbed().fit_transform(A1)
X2 = AdjacencySpectralEmbed().fit_transform(A2)
return X1, X2
def fit(seed):
np.random.seed(seed)
warnings.filterwarnings("ignore")
A1 = sbm(cn, B)
A2 = sbm(cm, B)
ldt = LatentDistributionTest(n_components=2, method="dcorr")
p = ldt.fit(A1, A2)
return p
def run_sim(Bx, By, n_components, n_bootstraps, sizes, seed):
np.random.seed(seed)
A0 = sbm(sizes, Bx, loops=False)
A1 = sbm(sizes, Bx, loops=False)
A2 = sbm(sizes, By, loops=False)
spt_null = SemiparametricTest(n_components=n_components,
n_bootstraps=n_bootstraps)
spt_alt = SemiparametricTest(n_components=n_components,
n_bootstraps=n_bootstraps)
spt_null.fit(A0, A1)
spt_alt.fit(A0, A2)
return (spt_null, spt_alt)
def generate_data():
np.random.seed(1)
p1 = [[0.2, 0.1], [0.1, 0.2]]
p2 = [[0.1, 0.2], [0.2, 0.1]]
n = [50, 50]
g1 = [sbm(n, p1) for _ in range(20)]
g2 = [sbm(n, p2) for _ in range(20)]
g = g1 + g2
y = ["0"] * 20 + ["1"] * 20
return g, y
def test_SBM_epsilon(self):
np.random.seed(12345678)
B1 = np.array([[0.5, 0.2], [0.2, 0.5]])
B2 = np.array([[0.7, 0.2], [0.2, 0.7]])
b_size = 200
A1 = sbm(2 * [b_size], B1)
A2 = sbm(2 * [b_size], B1)
A3 = sbm(2 * [b_size], B2)
npt_null = NonparametricTest(n_components=2, n_bootstraps=100)
npt_alt = NonparametricTest(n_components=2, n_bootstraps=100)
p_null = npt_null.fit(A1, A2)
p_alt = npt_alt.fit(A1, A3)
self.assertTrue(p_null > 0.05)
self.assertTrue(p_alt <= 0.05)
def test_SBM_epsilon(self):
np.random.seed(12345678)
B1 = np.array([[0.5, 0.2], [0.2, 0.5]])
B2 = np.array([[0.7, 0.2], [0.2, 0.7]])
b_size = 200
A1 = sbm(2 * [b_size], B1)
A2 = sbm(2 * [b_size], B1)
A3 = sbm(2 * [b_size], B2)
spt_null = LatentPositionTest(n_components=2, n_bootstraps=100)
spt_alt = LatentPositionTest(n_components=2, n_bootstraps=100)
p_null = spt_null.fit_predict(A1, A2)
p_alt = spt_alt.fit_predict(A1, A3)
self.assertTrue(p_null > 0.05)
self.assertTrue(p_alt <= 0.05)
def generate_cyclops(X, n, pi, density=None, density_params=[0,1], acorn=None):
if acorn is None:
acorn = np.random.randint(10**6)
np.random.seed(acorn)
counts = np.random.multinomial(n, [pi, 1 - pi]).astype(int)
if density is None:
density = np.random.uniform
U = sample(counts[0], density, density_params)
X_L = get_latent_positions(U)
else:
# U = sample(counts[0], density, density_params)
density_params = np.array(density_params)
d = len(density_params)
if density_params.ndim == 1:
pass
else:
X_temp = np.stack([sample(counts[0], density, density_params[i]) for i in range(d)], axis=1)
quad = np.sum(np.array([3, 3])*X_temp[:,:2]**2, axis=1)[:, np.newaxis]
print(quad, X_temp[0, 0], X_temp[0, 1], X_temp[0, 0]**2 + X_temp[0, 1]**2)
X_L = np.concatenate((X_temp[:,:2], quad), axis=1)
X = X[:, np.newaxis].T
All_X = np.concatenate((X_L, X), axis = 0)
P = All_X @ All_X.T
A = sbm(np.concatenate((np.ones(counts[0]).astype(int), [counts[1]])), P)
return A, counts
def setup_class(cls):
estimator = SBMEstimator(directed=True, loops=False)
B = np.array([[0.9, 0.1], [0.1, 0.9]])
g = sbm([50, 50], B, directed=True)
labels = _n_to_labels([50, 50])
p_mat = _block_to_full(B, labels, (100, 100))
p_mat -= np.diag(np.diag(p_mat))
cls.estimator = estimator
cls.p_mat = p_mat
cls.graph = g
cls.labels = labels
def get_B_and_weight_vec(n, pin=0.5, pout=0.01, mu_in=8, mu_out=2):
p = []
wt = []
wtargs = []
for i in range(len(n)):
sub_p = []
sub_wt = []
sub_wtargs = []
for j in range(len(n)):
sub_wt.append(normal)
if i == j:
sub_p.append(pin)
sub_wtargs.append(dict(loc=mu_in, scale=1))
else:
sub_p.append(pout)
sub_wtargs.append(dict(loc=mu_out, scale=1))
wt.append(sub_wt)
p.append(sub_p)
wtargs.append(sub_wtargs)
G = sbm(n=n, p=p, wt=wt, wtargs=wtargs)
N = len(G)
E = int(len(np.argwhere(G > 0)) / 2)
# B = np.zeros((E, N))
cnt = 0
weight_vec = np.zeros(E)
row = []
col = []
data = []
for item in np.argwhere(G > 0):
i, j = item
if i > j:
continue
if i == j:
print('nooooo')
# B[cnt, i] = 1
# B[cnt, j] = -1
row.append(cnt)
col.append(i)
data.append(1)
row.append(cnt)
col.append(j)
data.append(-1)
weight_vec[cnt] = abs(G[i, j])
cnt += 1
B = csr_matrix((data, (row, col)), shape=(E, N))
return B, weight_vec
def __init__(self, N):
#split in log(N) groups
K = math.floor(math.log(N))
group_sizes = [math.floor(N / K)] * K
group_sizes[0] += N - sum(group_sizes)
#Make P
P = np.full((K, K), .025)
np.fill_diagonal(P, .3)
#get G
self.groups = np.repeat(list(range(K)), group_sizes)
self.adj_matrix = sbm(n=group_sizes, p=P)
def test_SBM_dcorr(self):
for test in self.tests.keys():
np.random.seed(12345678)
B1 = np.array([[0.5, 0.2], [0.2, 0.5]])
B2 = np.array([[0.7, 0.2], [0.2, 0.7]])
b_size = 200
A1 = sbm(2 * [b_size], B1)
A2 = sbm(2 * [b_size], B1)
A3 = sbm(2 * [b_size], B2)
ldt_null = LatentDistributionTest(test,
self.tests[test],
n_components=2,
n_bootstraps=100)
ldt_alt = LatentDistributionTest(test,
self.tests[test],
n_components=2,
n_bootstraps=100)
p_null = ldt_null.fit_predict(A1, A2)
p_alt = ldt_alt.fit_predict(A1, A3)
self.assertTrue(p_null > 0.05)
self.assertTrue(p_alt <= 0.05)
def test_SBM_fit_supervised(self):
np.random.seed(8888)
B = np.array([
[0.9, 0.2, 0.05, 0.1],
[0.1, 0.7, 0.1, 0.1],
[0.2, 0.4, 0.8, 0.5],
[0.1, 0.2, 0.1, 0.7],
])
n = np.array([500, 500, 250, 250])
g = sbm(n, B, directed=True, loops=False)
sbe = SBMEstimator(directed=True, loops=False)
labels = _n_to_labels(n)
sbe.fit(g, y=labels)
B_hat = sbe.block_p_
assert_allclose(B_hat, B, atol=0.01)
def get_B_and_weight_vec(n, pin=0.5, pout=0.01, mu_in=8, mu_out=2):
p = []
wt = []
wtargs = []
for i in range(len(n)):
sub_p = []
sub_wt = []
sub_wtargs = []
for j in range(len(n)):
sub_wt.append(normal)
if i == j:
sub_p.append(pin)
sub_wtargs.append(dict(loc=mu_in, scale=1))
else:
sub_p.append(pout)
sub_wtargs.append(dict(loc=mu_out, scale=1))
wt.append(sub_wt)
p.append(sub_p)
wtargs.append(sub_wtargs)
G = sbm(n=n, p=p, wt=wt, wtargs=wtargs)
N = len(G)
E = int(len(np.argwhere(G > 0)) / 2)
B = np.zeros((E, N))
weight_vec = np.zeros(E)
cnt = 0
for item in np.argwhere(G > 0):
i, j = item
if i > j:
continue
if i == j:
print('nooooo')
B[cnt, i] = 1
B[cnt, j] = -1
weight_vec[cnt] = abs(G[i, j])
cnt += 1
return B, weight_vec
return avg_score, test_results
#Testing
if __name__ == '__main__':
import numpy as np
from graspy.embed import MultipleASE
from graspy.simulations import sbm
from graspy.plot import heatmap, pairplot
n_verts = 100
p = 0.8
labels_sbm = n_verts * [0] + n_verts * [1]
P = np.array([[p, 1.0 - p], [1.0 - p, p]])
undirected_sbms = []
for i in range(32):
undirected_sbms.append(sbm(2 * [n_verts], P))
def plotSVC(Xhat, clf):
h = 0.0002
x_min, x_max = Xhat[:, 0].min() - 0.01, Xhat[:, 0].max() + 0.01
y_min, y_max = Xhat[:, 1].min() - 0.01, Xhat[:, 1].max() + 0.01
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
import matplotlib
matplotlib.use('QT5Agg')
import matplotlib.pyplot as plt
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
plt.subplots(figsize=(10, 10))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
# #
n_blocks = 4
n_per_comm = 50
n_verts = n_blocks * n_per_comm
comm_proportions = n_blocks * [n_per_comm]
low_p = 0.02
p_mat = np.array(
[
[0.5, low_p, low_p, low_p],
[low_p, 0.4, low_p, low_p],
[low_p, low_p, 0.55, low_p],
[low_p, low_p, low_p, 0.45],
]
)
A, labels = sbm(comm_proportions, p_mat, return_labels=True)
heatmap(A, inner_hier_labels=labels, cbar=False)
# %% [markdown]
# # Compute some Laplacians
# The unnormalized graph Laplacian
L = unnormalized_laplacian(A)
heatmap(L, title="Unnormalized Graph Laplacian")
# L should be strictly PSD
evals, evecs = eig(L)
#%% %matplotlib inline from graspy.plot import * from graspy.simulations import sbm from graspy.embed import AdjacencySpectralEmbed import numpy as np import matplotlib.pyplot as plt import seaborn as sns g = sbm([100, 100], [[0.8, 0.2], [0.2, 0.8]]) ase = AdjacencySpectralEmbed() X = ase.fit_transform(g) labels = 25 * [0] + 25 * [1] + 25 * [2] + 24 * [-1] + [-2] # pairplot(X, size=50, alpha=0.6) plt.show()
import numpy as np
from graspy.utils import to_laplace
import matplotlib as mpl
sns.set_context("talk")
mpl.rcParams["axes.spines.right"] = False
mpl.rcParams["axes.spines.top"] = False
# %% [markdown]
# #
n_per_comm = [100, 100, 100]
n_verts = np.sum(n_per_comm)
block_probs = np.array([[0.4, 0.1, 0.1], [0.1, 0.4, 0.1], [0.1, 0.1, 0.4]])
adj, labels = sbm(n_per_comm, block_probs, return_labels=True)
fig, axs = plt.subplots(1, 2, figsize=(10, 5))
sns.heatmap(
block_probs, annot=True, cmap="RdBu_r", center=0, square=True, ax=axs[0], cbar=False
)
heatmap(adj, inner_hier_labels=labels, ax=axs[1], cbar=False)
#%%
I_DAD = to_laplace(adj, form="I-DAD")
DAD = to_laplace(adj, form="DAD")
fig, axs = plt.subplots(1, 2, figsize=(10, 5))
heatmap_kws = dict(inner_hier_labels=labels, cbar=False)
heatmap(I_DAD, ax=axs[0], **heatmap_kws)
# %% [markdown]
# ## Generate a "perfect" feedforward network (stochastic block model)
low_p = 0
diag_p = 0
feedforward_p = 0.2
community_sizes = 5 * [100]
B = get_feedforward_B(low_p, diag_p, feedforward_p)
plt.figure(figsize=(10, 10))
plt.title("Feedforward SBM block probability matrix")
sns.heatmap(B, annot=True, square=True, cmap="Reds", cbar=False)
plt.show()
A, labels = sbm(community_sizes,
B,
directed=True,
loops=False,
return_labels=True)
labels = labels.astype(str)
heatmap(
A,
cbar=False,
inner_hier_labels=labels,
title="Feedforward SBM sampled adjacency matrix",
)
plt.show()
# %% [markdown]
# ## Compute the signal flow metrix on the perfect feedforward network
# The energy function that this metric optimizes is for any pair of vertices, make the
# signal flow metric for node $i$ ($z_i$), equal to one greater than that for node $j$
# ($z_j$) if node $i$ is above node $j$ in the hierarchy. The basic intuition is that
def simulation(n,
pi,
normal_params,
beta_params,
cond_ind=True,
errors=None,
smooth=False,
acorn=None):
#- Type checks
if isinstance(normal_params, list):
sbm_check = False
# there are other checks to do..
elif isinstance(normal_params, np.ndarray):
if normal_params.ndim is 2:
if np.sum(normal_params == normal_params.T) == np.prod(
normal_params.shape):
sbm_check = True
else:
msg = 'if normal_params is a 2 dimensional array it must be symmetric'
raise ValueError(msg)
else:
msg = 'if normal_params is an array, it must be a 2 dimensional array'
raise TypeError(msg)
else:
msg = 'normal_params must be either a list or a 2 dimensional array'
raise TypeError(msg)
if acorn is None:
acorn = np.random.randint(10**6)
np.random.seed(acorn)
#- Multinomial trial
counts = np.random.multinomial(n, [pi, 1 - pi])
#- Hard code the number of blocks
K = 2
#- Set labels
labels = np.concatenate((np.zeros(counts[0]), np.ones(counts[1])))
#- number of seeds = n_{i}/10
n_seeds = np.round(0.1 * counts).astype(int)
#- Set training and test data
class_train_idx = [
range(np.sum(counts[:k]),
np.sum(counts[:k]) + n_seeds[k]) for k in range(K)
]
train_idx = np.concatenate((class_train_idx)).astype(int)
test_idx = [k for k in range(n) if k not in train_idx]
#- Total number of seeds
m = np.sum(n_seeds)
#- estimate class probabilities
pi_hats = n_seeds / m
#- Sample from beta distributions
beta_samples = beta_sampler(counts, beta_params)
Z = beta_samples
#- Sample from multivariate normal or SBM either independently of Zs or otherwise
if cond_ind:
if sbm_check:
A = sbm(counts, normal_params)
ase_obj = ASE(n_elbows=1)
X = ase_obj.fit_transform(A)
else:
X = MVN_sampler(counts, normal_params)
if len(normal_params[0][0]) is 1:
X = X[:, np.newaxis]
else:
if sbm_check:
P = blowup(
normal_params, counts
) # A big version of B to be able to change connectivity probabilities of individual nodes
scales = np.prod(Z, axis=1)**(
1 / Z.shape[1]
) # would do just the outer product, but if the Z's are too small we risk not being connected
new_P = P * (scales @ scale.T) # new probability matrix
A = sbm(np.ones(n).astype(int), new_P)
ase_obj = ASE(n_elbows=1)
X = ase_obj.fit_transform(A)
else:
X = conditional_MVN_sampler(Z=Z,
rho=1,
counts=counts,
params=normal_params,
seed=None)
if len(normal_params[0][0]) is 1:
X = X[:, np.newaxis]
XZ = np.concatenate((X, Z), axis=1)
#- Estimate normal parameters using seeds
params = []
for i in range(K):
temp_mu, temp_cov = estimate_normal_parameters(X[class_train_idx[i]])
params.append([temp_mu, temp_cov])
#- Using conditional indendence assumption (RF, KNN used for posterior estimates)
if errors is None:
errors = [[] for i in range(5)]
rf1 = RF(n_estimators=100,
max_depth=int(np.round(np.log(Z[train_idx].shape[0]))))
rf1.fit(Z[train_idx], labels[train_idx])
knn1 = KNN(n_neighbors=int(np.round(np.log(Z[train_idx].shape[0]))))
knn1.fit(Z[train_idx], labels[train_idx])
if smooth:
temp_pred = classify(X[test_idx], Z[test_idx], params, rf1, m=m)
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[0].append(temp_error)
temp_pred = classify(X[test_idx], Z[test_idx], params, knn1, m=m)
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[1].append(temp_error)
else:
temp_pred = classify(X[test_idx], Z[test_idx], params, rf1)
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[0].append(temp_error)
knn1 = KNN(n_neighbors=int(np.round(np.log(m))))
knn1.fit(Z[train_idx], labels[train_idx])
temp_pred = classify(X[test_idx], Z[test_idx], params, knn1)
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[1].append(temp_error)
temp_pred = QDA(X[test_idx], pi_hats, params)
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[2].append(temp_error)
#- Not using conditional independence assumption (RF, KNN used for classification)
XZseeds = np.concatenate((X[train_idx], Z[train_idx]), axis=1)
rf2 = RF(n_estimators=100, max_depth=int(np.round(np.log(m))))
rf2.fit(XZ[train_idx], labels[train_idx])
temp_pred = rf2.predict(XZ[test_idx])
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[3].append(temp_error)
knn2 = KNN(n_neighbors=int(np.round(np.log(m))))
knn2.fit(XZ[train_idx], labels[train_idx])
temp_pred = knn2.predict(XZ[test_idx])
temp_error = 1 - np.sum(temp_pred == labels[test_idx]) / len(test_idx)
errors[4].append(temp_error)
temp_accuracy = GCN(adj, features, train_idx, labels)
temp_error = 1 - temp_accuracy
errors[5].append(temp_error)
return errors
from numpy.core.defchararray import replace
import pandas as pd
import seaborn as sns
from graspy.embed import AdjacencySpectralEmbed
from graspy.plot import heatmap
from graspy.simulations import sbm
from numpy.core.shape_base import block
from sklearn.mixture import GaussianMixture
sns.set_context("talk")
n_per_comm = [1000, 1000, 1000]
n_verts = np.sum(n_per_comm)
block_probs = np.array([[0.5, 0.1, 0.1], [0.1, 0.5, 0.1], [0.1, 0.1, 0.5]])
adj, labels = sbm(n_per_comm, block_probs, return_labels=True)
# %%
ase = AdjacencySpectralEmbed(n_components=3)
Xhat = ase.fit_transform(adj)
# %%
# REF: Anton
def _fit_plug_in_variance_estimator(X):
"""
Takes in ASE of a graph and returns a function that estimates
the variance-covariance matrix at a given point using the
plug-in estimator from the RDPG Central Limit Theorem.
from SupervisedLearning import MASEPipeline
from sklearn.decomposition import PCA
from sklearn.neighbors import KNeighborsClassifier
#Testing
if __name__ == '__main__':
import numpy as np
from graspy.simulations import sbm
from graspy.plot import heatmap, pairplot
n_verts = 100
nums = 128
p1 = 0.8
p2 = 0.81
labels_sbm = nums * [1] + nums * [2]
P1 = np.array([[p1, 1.0-p1], [1.0-p1, p1]])
P2 = np.array([[p2, 1.0-p2], [1.0-p2, p2]])
undirected_sbms = []
for i in range(nums):
undirected_sbms.append(sbm(2 * [n_verts], P1))
for i in range(nums):
undirected_sbms.append(sbm(2 * [n_verts], P2))
G = np.array(undirected_sbms)
print(G.shape)
MASEP = MASEPipeline([('pca', PCA(n_components=4)) ,('knn', KNeighborsClassifier())])
MASEP.set_params(MASE__n_components=6, MASE__algorithm='full')
MASEP.fit(undirected_sbms, labels_sbm)
print(MASEP.predict(undirected_sbms))
cvs, _ = MASEP.cross_val_score(undirected_sbms, labels_sbm)
print(cvs)
n_blocks=n_blocks)
plt.figure(figsize=(10, 10))
sns.heatmap(block_probs, annot=True, cmap="Reds", cbar=False)
plt.title("Feedforward block probability matrix")
stashfig("ffw-B")
#%%
community_sizes = np.empty(2 * n_blocks, dtype=int)
n_feedforward = 100
n_feedback = 100
community_sizes[::2] = n_feedforward
community_sizes[1::2] = n_feedback
community_sizes = n_blocks * [n_feedforward]
labels = n_to_labels(community_sizes)
A = sbm(community_sizes, block_probs, directed=True, loops=False)
n_verts = A.shape[0]
perm_inds = np.random.permutation(n_verts)
A_perm = A[np.ix_(perm_inds, perm_inds)]
heatmap(A, cbar=False, title="Feedforward SBM")
stashfig("ffSBM")
heatmap(A_perm, cbar=False, title="Feedforward SBM, shuffled")
stashfig("ffSBM-shuffle")
true_z = signal_flow(A)
sort_inds = np.argsort(true_z)[::-1]
heatmap(
A[np.ix_(sort_inds, sort_inds)],
cbar=False,
def fit(seed):
warnings.filterwarnings("ignore")
np.random.seed(seed)
ldt = LatentDistributionTest(n_components=2, method="dcorr")
p = ldt.fit(A1, A2)
return p
for n in range(start, stop, diff):
ns.append(n)
for m in range(n, n + stop - start, diff):
print(f"Running tests for n={n}, m={m}")
cn = [n // k] * k
cm = [m // k] * k
A1 = sbm(cn, B)
A2 = sbm(cm, B)
type1_errors = 0
seeds = np.random.randint(0, 1e8, tests)
for p in range(tests):
out = Parallel(n_jobs=-2,
verbose=0)(delayed(fit)(seed) for seed in seeds)
out = np.array(out)
type1_errors += len(np.where(out < alpha)[0])
error = type1_errors / tests
temp.append(error)
ms.append(m - n)
error_list.append(temp)
"""The argument p is assumed to be some permutation of 0, 1, ..., len(p)-1.
Returns an array s, where s[i] gives the index of i in p.
"""
s = np.empty(p.size, p.dtype)
s[p] = np.arange(p.size)
return s
n = [50, 20, 20, 5, 5]
block_p = np.zeros((5, 5))
block_p += np.diag(0.5 * np.ones(5))
n_verts = 100
shuffle_inds = np.random.permutation(n_verts)
A = sbm(n, block_p)
B = A[np.ix_(shuffle_inds,
shuffle_inds)] # B is a permuted version of A (corr = 1)
faq = FastApproximateQAP(
max_iter=30,
eps=0.0001,
init_method="rand",
n_init=100,
shuffle_input=False,
maximize=True,
)
A_found, B_found = faq.fit_predict(A, B)
reverse_shuffle = invert_permutation(shuffle_inds)
feedforward_p,
n_blocks=n_blocks)
fig, axs = plt.subplots(1, 2, figsize=(20, 10))
sns.heatmap(block_probs,
annot=True,
cmap="Reds",
cbar=False,
ax=axs[0],
square=True)
axs[0].xaxis.tick_top()
axs[0].set_title("Block probability matrix", pad=25)
np.random.seed(88)
adj, labels = sbm(community_sizes,
block_probs,
directed=True,
loops=False,
return_labels=True)
n_verts = adj.shape[0]
adjplot(adj, sort_class=labels, cbar=False, ax=axs[1], square=True)
axs[1].set_title("Adjacency matrix", pad=25)
plt.tight_layout()
stashfig("sbm" + basename)
# %% [markdown]
# ##
currtime = time.time()
n_verts = len(adj)
#%%
from graspy.simulations import sbm
import numpy as np
from graspy.plot import heatmap, pairplot
n = np.array([100, 100, 100])
p = np.array([[0.3, 0.2, 0.1], [0.01, 0.2, 0.2], [0.02, 0.03, 0.1]])
dcs = []
for i in range(len(n)):
dc = np.random.beta(2, 5, n[i])
dc /= dc.sum()
dcs.append(dc)
dcs = np.concatenate(dcs)
adj, labels = sbm(n, p, directed=True, dc=dcs, return_labels=True)
heatmap(adj, cbar=False, sort_nodes=True, inner_hier_labels=labels)
#%%
from graspy.embed import AdjacencySpectralEmbed
ase = AdjacencySpectralEmbed(n_components=3)
embed = ase.fit_transform(adj)
embed = np.concatenate(embed, axis=-1)
#%%
pairplot(embed, labels=labels)
# %% [markdown]
# ##
norm_embed = embed / np.linalg.norm(embed, axis=1)[:, None]
import graspy
import matplotlib.pyplot as plt
import numpy as np
from sklearn.svm import SVC
from graspy.simulations import sbm
nums = 32
n = [25, 25]
P1 = [[.3, .1], [.1, .7]]
P2 = [[.3, .1], [.1, .3]]
labels = [1] * nums + [2] * nums
#labels = np.matrix([labels])
#labels = labels.transpose(1, 0)
np.random.seed(8)
Gs = []
for i in range(nums):
Gs.append(sbm(n, P1))
for i in range(nums):
Gs.append(sbm(n, P2))
def plotSVC(Xhat, clf):
h = 0.0002
x_min, x_max = Xhat[:, 0].min() - 0.01, Xhat[:, 0].max() + 0.01
y_min, y_max = Xhat[:, 1].min() - 0.01, Xhat[:, 1].max() + 0.01
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
import matplotlib
matplotlib.use('QT5Agg')
import matplotlib.pyplot as plt
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
plt.subplots(figsize=(10, 10))
from graspy.plot import *
from graspy.simulations import sbm
from graspy.embed import AdjacencySpectralEmbed
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
B = np.array([
[0, 0.2, 0.1, 0.1, 0.1],
[0.2, 0.8, 0.1, 0.3, 0.1],
[0.15, 0.1, 0, 0.05, 0.1],
[0.1, 0.1, 0.2, 1, 0.1],
[0.1, 0.2, 0.1, 0.1, 0.8],
])
g = sbm([10, 30, 50, 25, 25], B, directed=True)
ase = AdjacencySpectralEmbed()
X = ase.fit_transform(g)
labels2 = 40 * ["0"] + 100 * ["1"]
# pairplot(X, size=50, alpha=0.6)
labels1 = 10 * ["d"] + 30 * ["c"] + 50 * ["d"] + 25 * ["e"] + 25 * ["c"]
labels1 = np.array(labels1)
labels2 = np.array(labels2)
# plt.style.use(["seaborn",])
plt.style.use("seaborn-white")
heatmap(
g,
inner_hier_labels=labels1,
outer_hier_labels=labels2,
figsize=(20, 20),
label_fontsize=30,
# %% setting up the model
n = 1000
k = 4
expected_degree = 40
degree_corrections = np.random.lognormal(2, 1.5, size=(n))
community_sizes = np.full(k, n // k)
block_probs = np.full((k, k), 0.1)
block_probs[0, 0] = 0.9
block_probs[1, 1] = 0.7
block_probs[2, 2] = 0.5
block_probs[3, 3] = 0.3
block_heatmap(block_probs, title=r"$B$")
_, labels = sbm(
community_sizes, block_probs, directed=False, loops=False, return_labels=True
)
#%% rescaling to set the expected degree
block_p_mat = _block_to_full(block_probs, labels, (n, n))
unscaled_expected_degree = np.mean(np.sum(block_p_mat, axis=1))
scaling_factor = 40 / unscaled_expected_degree
print(f"Scaling factor: {scaling_factor:.3f}")
#%% [markdown]
# ## Sampling from the model
# Here I just sample a graph from the model (after rescaling to set the expected degree).
# Below I plot the adjacency matrix sorted by block and then by node degree within block.
# I also calculate the mean degree to show that it is close to what we specified.
#%% adjusting the degree correction params / rescaling, sampling a graph
for ul in np.unique(labels):
if weighted:
wt = n_comm * [n_comm * [np.random.poisson]]
lams = np.random.uniform(0.1, 0.3, size=(n_comm**2))
lams = lams.reshape(n_comm, n_comm)
lams[P != base_p] = P[P != base_p] * 5
wtargs = np.array([dict(lam=lam)
for lam in lams.ravel()]).reshape(n_comm, n_comm)
else:
lams = np.ones_like(P)
wtargs = None
wt = 1
adj, labels = sbm(n_per_comm,
P,
directed=True,
loops=False,
wt=wt,
wtargs=wtargs,
return_labels=True)
sns.set_context("talk", font_scale=0.5)
fig, axs = plt.subplots(1, 3, figsize=(16, 8))
sns.heatmap(
P,
annot=True,
square=True,
ax=axs[0],
cbar=False,
# cbar_kws=dict(shrink=0.7),
cmap="RdBu_r",
center=0,