def __call__(self, G, r):
# https://arxiv.org/pdf/0803.0929.pdf
a = 0
maxT = G
maxConductance = 0
vertex2id = {u: i for i, u in enumerate(G)}
A = np.zeros((len(vertex2id), len(vertex2id)))
for u, v in G.edges():
if u != v:
A[vertex2id[u]][vertex2id[v]] = 1
A[vertex2id[v]][vertex2id[u]] = 1
invD = np.diag((A.sum(axis=0) + 1.E-12)**(-1))
L = np.eye(len(vertex2id)) - invD**0.5 @ A @ invD**0.5
pseudoinverse = 0
eigenvalues, eigenvectors = np.linalg.eigh(L)
for eigenvalue, eigenvector in zip(eigenvalues, eigenvectors):
if eigenvalue > 1.E-12:
pseudoinverse += np.outer(eigenvector,
eigenvector) / eigenvalue
epsilon = 0.1
beta = 1 # 1+-epsilon factor approximation with probability 1-n**-beta (where n is the number of nodes)
k = int((4 + 2 * beta) * np.log(len(G)) /
(epsilon**2 / 2 - epsilon**3 / 3))
for repeat in range(10 * self.range_a):
if repeat % self.repeats == 0:
a += 1
Q = np.random.binomial(1, 0.5, (k, len(G))) * 2 - 1
Q = Q / (float(k)**0.5)
Z = Q @ pseudoinverse
if random() < 1. / self.repeats:
a += 1
T = nx.DiGraph()
Y = float(len(G)) / sum(
np.linalg.norm(Z[vertex2id[u], :] - Z[vertex2id[v], :])**2
for u, v in G.edges()) / a
for u, v in G.edges():
resistance = np.linalg.norm(Z[vertex2id[u], :] -
Z[vertex2id[v], :])**2
if random() < Y / resistance:
T.add_edge(u, v)
if r not in T:
T = nx.DiGraph()
T.add_node(r)
continue
else:
T = nx.traversal.bfs_tree(T, r)
cond = conductance(G, T)
if cond > maxConductance:
maxConductance = cond
maxT = T
#if maxT != G:
# return SOTASparsifier()(maxT, r)
return maxT
def core(G, r, trace_method, eps=1.E-6, starting_a=-1, deflation_strategy=1):
tr_cond = starting_a
tr = None
found_a = starting_a
while True:
a = tr_cond + 1 - eps
next_tr = trace_method(G, r, a)
tr_cond = conductance(G, next_tr)
if next_tr is None or len(next_tr) <= 1 or a <= found_a:
break
found_a = a
tr = next_tr
if tr is None:
tr = nx.DiGraph()
tr.add_node(r)
#print('Bounds', len(tr), 0.5*(sum(max(G.out_degree(v)-a*deflation_strategy,0) for v in G if v not in tr))/len(tr))
return tr
def sparsifier(G, r):
# https://arxiv.org/pdf/0808.4134.pdf
max_cond, max_tree = 0, None
max_deg = max(G.degree(v) for v in G)
#print('max deg', max_deg)
for Y in np.arange(0, 1, 0.01):
for _ in range(1):
subgraph = nx.DiGraph([
(u, v) for u, v in G.edges()
if random() < Y * max_deg / min(G.degree(u), G.degree(v))
])
#tree = subgraph
tree = bfs_tree(subgraph, r)
cond = conductance(G, tree)
if cond > max_cond:
max_cond, max_tree = cond, tree
return trivial_graph(r) if max_tree is None else max_tree
def eigenreductor(G, r):
vertex2id = {u: i for i, u in enumerate(G)}
eigenvalues, eigenvectors = np.linalg.eigh(laplacian(G, vertex2id))
eigorder = sorted(list(range(len(eigenvalues))),
key=lambda i: -eigenvalues[i])
max_cond, max_tree = 0, None
original_sum = eigenvalues.sum()
largest = 0
smallest = len(eigenvalues) - 1
for i in range(len(eigenvalues) - 1):
if eigenvalues[eigorder[smallest]] / (eigenvalues.sum() - eigenvalues[
eigorder[largest]]) > eigenvalues[eigorder[smallest - 1]] / (
eigenvalues.sum() - eigenvalues[eigorder[smallest]]):
changed = (eigorder[largest], eigenvalues[eigorder[largest]])
eigenvalues[eigorder[largest]] = 0
largest += 1
else:
changed = (eigorder[smallest], eigenvalues[eigorder[smallest]])
eigenvalues[eigorder[smallest]] = 0
smallest -= 1
Lapprox = eigenvectors @ np.diag(
eigenvalues * original_sum /
eigenvalues.sum()) @ eigenvectors.transpose()
#for Y in np.arange(0, 1, 0.1):
subgraph = nx.DiGraph([
(u, v) for u, v in G.edges()
if random() < abs(Lapprox[vertex2id[u], vertex2id[v]])
])
if r not in subgraph:
eigenvalues[changed[0]] = changed[1]
continue
tree = bfs_tree(subgraph, r)
cond = conductance(G, tree)
if cond > max_cond:
max_cond, max_tree = cond, tree
return trivial_graph(r) if max_tree is None else max_tree
#"elod_core": lambda G,r: conductance.trace.core(G, r, conductance.trace.maxELOD),
#"greedy_clever": lambda G,r: conductance.spectral.greedy(G, conductance.trace.core(G, r, conductance.trace.cleverRPCST)),
#"greedy_recursive": lambda G,r: conductance.spectral.greedy_recursive(G, [r], [lambda a,b: a-(1+sigma)/10.*alpha*b for sigma in range(10)])
}
# = {"ACM", "ANT", "DBLP", "Log4J", "Pubmed`", "Squirrel"}
datasets = {"ANT1.1": "data/ant_1.1_features.csv", }
for dataset in datasets:
G = import_graph(datasets[dataset], directed=False).to_directed()
results = {method: list() for method in implementation}
nodes = [v for v in G if G.out_degree[v]>=2]
for i in range(1):# 200 to get Nemenyi statistical significance for sure
#print("\n-----------------------")
if len(nodes)==0:
continue
r = nodes[(int)(random()*len(nodes))]
for method in implementation:
subgraph = implementation[method](G, r)
results[method].append(measures.conductance(G, subgraph))
#print(method, len(subgraph))
#for method in implementation:
# print(method, ' = ', [round(v) for v in results[method]], '; %', sum(results[method])/len(results[method]))
ranks, crit = friedman_ranks(results)
print(dataset, "("+str(int(0.5+crit*10)/10.0)+")", "&", " & ".join(str(int(0.5+sum(results[method])/len(results[method])))+" ("+str(int(0.5+ranks[method]*10)/10.0)+")" for method in ranks) )