def run_sim(seed):
A1, A2 = sbm_corr(block_members,
block_probs,
rho,
directed=directed,
loops=loops)
node_shuffle_input = np.random.permutation(n)
A2_shuffle = A2[np.ix_(node_shuffle_input, node_shuffle_input)]
node_unshuffle_input = np.array(range(n))
node_unshuffle_input[node_shuffle_input] = np.array(range(n))
W1 = np.sort(random.sample(list(range(n)), i))
W1 = W1.astype(int)
W2 = np.array(node_unshuffle_input[W1])
faq = GMP(gmp=True)
faq = faq.fit(A1, A2_shuffle, W1, W2)
return match_ratio(faq.perm_inds_, node_unshuffle_input)
def run_sim(seed):
A1, A2 = sbm_corr(
block_members, block_probs, rho, directed=directed, loops=loops
)
score = 0
res_opt = None
score_ss = 0
res_opt_ss = None
for j in range(t):
res = quadratic_assignment_sim(A1,A2, sim=False, maximize=True, options={'seed':seed[j]})
if res['score']>score:
res_opt = res
score = res['score']
res = quadratic_assignment_sim(A1,A2, sim=True, maximize=True, options={'seed':seed[j]})
if res['score']>score_ss:
res_opt_ss = res
score_ss = res['score']
ratio = match_ratio(res_opt['col_ind'], n)
score = res_opt['score']
ratio_ss = match_ratio(res_opt_ss['col_ind'], n)
score_ss = res_opt_ss['score']
res = quadratic_assignment_sim(A1,A2, sim=False, maximize=True, options={'shuffle_input':False})
ratio_opt = match_ratio(res['col_ind'], n)
score_opt = res['score']
res = quadratic_assignment_sim(A1,A2, sim=True, maximize=True, options={'shuffle_input':False})
ratio_opt_ss = match_ratio(res['col_ind'], n)
score_opt_ss = res['score']
return ratio, score, ratio_ss, score_ss, ratio_opt, score_opt, ratio_opt_ss, score_opt_ss
# ##
show_adjs = False
B = np.array([[0.3, 0.7], [0.05, 0.3]])
rho = 0.9
n_per_block = 10
n_blocks = len(B)
comm = n_blocks * [n_per_block]
n_init = 50
eps = 1.0
n_samples = 20
rows = []
for i in range(n_samples):
A1, A2 = sbm_corr(comm, B, rho)
max_score = np.trace(A1 @ A2.T)
shuffle_inds = np.random.choice(len(A1), replace=False, size=len(A1))
A2_shuffle = A2[np.ix_(shuffle_inds, shuffle_inds)]
if show_adjs:
fig, axs = plt.subplots(1, 4, figsize=(10, 5))
heatmap(A1, ax=axs[0], cbar=False, title="Graph 1")
heatmap(A2, ax=axs[1], cbar=False, title="Graph 2")
heatmap(A1 - A2, ax=axs[2], cbar=False, title="Diff (G1 - G2)")
heatmap(A2_shuffle, ax=axs[3], cbar=False, title="Graph 2 shuffled")
P = np.zeros_like(A1)
P[np.arange(len(P)), shuffle_inds] = 1
fig, axs = plt.subplots(1, 4, figsize=(20, 5))
block_probs = np.array([[0.7, 0.3, 0.4], [0.3, 0.7, 0.3], [0.4, 0.3, 0.7]])
# plot block probs
fig, ax = plt.subplots(1, 1, figsize=(4, 4))
sns.heatmap(block_probs,
cbar=False,
annot=True,
square=True,
cmap="Reds",
ax=ax)
ax.set_title("SBM block probabilities")
# generate graphs
A1, A2 = sbm_corr(block_members,
block_probs,
rho,
directed=directed,
loops=loops)
fig, axs = plt.subplots(1, 3, figsize=(10, 5))
heatmap(A1, ax=axs[0], cbar=False, title="Graph 1")
heatmap(A2, ax=axs[1], cbar=False, title="Graph 2")
heatmap(A1 - A2, ax=axs[2], cbar=False, title="Diff (G1 - G2)")
# shuffle for testing
node_shuffle_input = np.random.permutation(n_verts)
A2_shuffle = A2[np.ix_(node_shuffle_input, node_shuffle_input)]
node_unshuffle_input = np.array(range(n_verts))
node_unshuffle_input[node_shuffle_input] = np.array(range(n_verts))
# plot shuffled
fig, axs = plt.subplots(1, 3, figsize=(10, 5))
def run_sim(seed):
A1, A2 = sbm_corr(block_members,
block_probs,
rho,
directed=directed,
loops=loops)
score = 0
res_opt = None
score_ss = 0
res_opt_ss = None
ase = AdjacencySpectralEmbed(n_components=3, algorithm='truncated')
Xhat1 = ase.fit_transform(A1)
Xhat2 = ase.fit_transform(A2)
if flip == 'median':
xhh1, xhh2 = _median_sign_flips(Xhat1, Xhat2)
S = xhh1 @ xhh2.T
elif flip == 'jagt':
sp = SeedlessProcrustes().fit(Xhat1, Xhat2)
xhh1 = Xhat1 @ sp.Q
xhh2 = Xhat2
S = xhh1 @ xhh2.T
else:
S = None
for j in range(t):
res = quadratic_assignment_sim(A1,
A2,
True,
options={'seed': seed[j]})
if res['score'] > score:
res_opt = res
score = res['score']
res = quadratic_assignment_sim(A1,
A2,
True,
S,
options={'seed': seed[j]})
if res['score'] > score_ss:
res_opt_ss = res
score_ss = res['score']
ratio = match_ratio(res_opt['col_ind'], n)
score = res_opt['score']
ratio_ss = match_ratio(res_opt_ss['col_ind'], n)
score_ss = res_opt_ss['score']
res = quadratic_assignment_sim(A1,
A2,
True,
options={'shuffle_input': False})
ratio_opt = match_ratio(res['col_ind'], n)
score_opt = res['score']
res = quadratic_assignment_sim(A1,
A2,
True,
S,
options={'shuffle_input': False})
ratio_opt_ss = match_ratio(res['col_ind'], n)
score_opt_ss = res['score']
return ratio, score, ratio_ss, score_ss, ratio_opt, score_opt, ratio_opt_ss, score_opt_ss
def run_sim(seed):
A1, A2 = sbm_corr(block_members,
block_probs,
rho,
directed=directed,
loops=loops)
score_10 = 0
res_10_opt = None
score_3 = 0
res_3_opt = None
ase3 = AdjacencySpectralEmbed(n_components=3,
algorithm='truncated')
Xhat31 = ase3.fit_transform(A1)
Xhat32 = ase3.fit_transform(A2)
ase10 = AdjacencySpectralEmbed(n_components=10,
algorithm='truncated')
Xhat101 = ase10.fit_transform(A1)
Xhat102 = ase10.fit_transform(A2)
if flip == 'median':
xhh31, xhh32 = _median_sign_flips(Xhat31, Xhat32)
xhh101, xhh102 = _median_sign_flips(Xhat101, Xhat102)
elif flip == 'jagt':
sp3 = SeedlessProcrustes(init='sign_flips').fit(Xhat31, Xhat32)
xhh31 = Xhat31 @ sp3.Q_
xhh32 = Xhat32
sp10 = SeedlessProcrustes(init='sign_flips').fit(
Xhat101, Xhat102)
xhh101 = Xhat101 @ sp10.Q_
xhh102 = Xhat102
else:
S = None
if sim == 'mult':
S3 = xhh31 @ xhh32.T
S10 = xhh101 @ xhh102.T
elif sim == 'pdist':
S3 = pdist_youngser(xhh31, xhh32)
S10 = pdist_youngser(xhh101, xhh102)
for j in range(t):
res = quadratic_assignment_sim(A1,
A2,
True,
S3,
options={'seed': seed[j]})
if res['score'] > score_3:
res_3_opt = res
score_3 = res['score']
res = quadratic_assignment_sim(A1,
A2,
True,
S10,
options={'seed': seed[j]})
if res['score'] > score_10:
res_10_opt = res
score_10 = res['score']
ratio_3 = match_ratio(res_3_opt['col_ind'], n)
score_3 = res_3_opt['score']
ratio_10 = match_ratio(res_10_opt['col_ind'], n)
score_10 = res_10_opt['score']
return ratio_3, score_3, ratio_10, score_10