def test_marginalized_graph_kernel_2nd_launch(benchmark, batch):
graphs = [Graph.from_networkx(g, weight='weight')
for g in make_graphs(batch, 48)]
knode = TensorProduct(label=KroneckerDelta(0.5))
kedge = TensorProduct(label=KroneckerDelta(0.5))
kernel = MarginalizedGraphKernel(knode, kedge)
def fun():
kernel(graphs, nodal=False)
benchmark.pedantic(fun, iterations=3, rounds=3, warmup_rounds=0)
def test_mlgk_typecheck():
node_kernel = Constant(1.0)
edge_kernel = Constant(1.0)
mlgk = MarginalizedGraphKernel(node_kernel, edge_kernel, q=0.5)
G = [
Graph.from_networkx(unlabeled_graph1),
Graph.from_networkx(labeled_graph1),
Graph.from_networkx(weighted_graph1, weight='w')
]
with pytest.raises(TypeError):
mlgk([G[0], G[1]])
with pytest.raises(TypeError):
mlgk([G[0], G[2]])
with pytest.raises(TypeError):
mlgk([G[1], G[2]])
with pytest.raises(TypeError):
mlgk([G[1], G[0]])
with pytest.raises(TypeError):
mlgk([G[2], G[0]])
with pytest.raises(TypeError):
mlgk([G[2], G[1]])
def test_mlgk_self_loops():
kedge = Constant(1.0)
knode = Constant(1.0)
q = 0.1
mlgk = MarginalizedGraphKernel(knode, kedge, q=q)
np.random.seed(2)
for i in range(10):
n = np.random.randint(4, 20)
A = np.random.randn(n, n)
A = A + A.T
G = [Graph.from_networkx(nx.from_numpy_array(A), weight='weight')]
K = mlgk(G).item()
K0 = MLGK(G[0], knode, kedge, q, q, nodal=False)
assert (K == pytest.approx(K0, 5e-4))
def test_mlgk_fixed_hyperparameters():
g = nx.Graph()
g.add_node(0, feature=0)
g.add_node(1, feature=1)
g.add_node(2, feature=0)
g.add_edge(0, 1, attribute=1.0)
g.add_edge(0, 2, attribute=2.0)
G = [Graph.from_networkx(g)]
knodeV = TensorProduct(feature=KroneckerDelta(0.5))
knodeF = TensorProduct(feature=KroneckerDelta(0.5, h_bounds='fixed'))
kedgeV = TensorProduct(attribute=SquareExponential(1.0))
kedgeF = TensorProduct(
attribute=SquareExponential(1.0, length_scale_bounds='fixed'))
kernelVV = MarginalizedGraphKernel(knodeV, kedgeV)
kernelVF = MarginalizedGraphKernel(knodeV, kedgeF)
kernelFV = MarginalizedGraphKernel(knodeF, kedgeV)
kernelFF = MarginalizedGraphKernel(knodeF, kedgeF)
assert (len(kernelVV.theta) == len(kernelVF.theta) + 1)
assert (len(kernelVV.theta) == len(kernelFV.theta) + 1)
assert (len(kernelVV.theta) == len(kernelFF.theta) + 2)
assert (len(kernelVV.bounds) == len(kernelVF.bounds) + 1)
assert (len(kernelVV.bounds) == len(kernelFV.bounds) + 1)
assert (len(kernelVV.bounds) == len(kernelFF.bounds) + 2)
Rvv, dRvv = kernelVV(G, eval_gradient=True)
Rvf, dRvf = kernelVF(G, eval_gradient=True)
Rfv, dRfv = kernelFV(G, eval_gradient=True)
Rff, dRff = kernelFF(G, eval_gradient=True)
assert (Rvv == pytest.approx(Rvf))
assert (Rvv == pytest.approx(Rfv))
assert (Rvv == pytest.approx(Rff))
assert (dRvv.shape[2] == dRvf.shape[2] + 1)
assert (dRvv.shape[2] == dRfv.shape[2] + 1)
assert (dRvv.shape[2] == dRff.shape[2] + 2)
assert (dRvv[:, :, kernelVF.active_theta_mask] == pytest.approx(dRvf))
assert (dRvv[:, :, kernelFV.active_theta_mask] == pytest.approx(dRfv))
assert (dRvv[:, :, kernelFF.active_theta_mask] == pytest.approx(dRff))
def test_mlgk_large():
g = nx.Graph()
n = 24
for i, row in enumerate(np.random.randint(0, 2, (n, n))):
g.add_node(i, type=0)
for j, pred in enumerate(row[:i]):
if pred:
g.add_edge(i, j, weight=1)
dfg = Graph.from_networkx(g, weight='weight')
q = 0.5
node_kernel = TensorProduct(type=KroneckerDelta(1.0))
edge_kernel = Constant(1.0)
mlgk = MarginalizedGraphKernel(node_kernel, edge_kernel, q=q)
dot = mlgk([dfg])
gold = MLGK(dfg, node_kernel, edge_kernel, q, q)
assert (dot.shape == (1, 1))
assert (dot.item() == pytest.approx(gold))
def test_mlgk_dtype():
g = nx.Graph()
n = 8
for i, row in enumerate(np.random.randint(0, 2, (n, n))):
g.add_node(i, type=0)
for j, pred in enumerate(row[:i]):
if pred:
g.add_edge(i, j, weight=1)
dfg = Graph.from_networkx(g, weight='weight')
q = 0.5
node_kernel = TensorProduct(type=KroneckerDelta(1.0))
edge_kernel = Constant(1.0)
for dtype in [np.float, np.float32, np.float64]:
mlgk = MarginalizedGraphKernel(node_kernel,
edge_kernel,
q=q,
dtype=dtype)
assert (mlgk([dfg]).dtype == dtype)
assert (mlgk.diag([dfg]).dtype == dtype)
g2.add_node(2) g2.add_edge(0, 1) g2.add_edge(1, 2) # 0 --- 1 # \ / # 2 g3 = nx.Graph() g3.add_node(0) g3.add_node(1) g3.add_node(2) g3.add_edge(0, 1) g3.add_edge(0, 2) g3.add_edge(1, 2) # define trivial node and edge kernelets knode = Constant(1.0) kedge = Constant(1.0) # compose the marginalized graph kernel and compute pairwise similarity mlgk = MarginalizedGraphKernel(knode, kedge, q=0.05) R = mlgk([Graph.from_networkx(g) for g in [g1, g2, g3]]) # normalize the similarity matrix d = np.diag(R)**-0.5 K = np.diag(d).dot(R).dot(np.diag(d)) # all entries should be approximately 1 plus round-off error print(K)
g1 = nx.Graph()
g1.add_node(0, category=(1, 2), symbol=1)
g1.add_node(1, category=(2, ), symbol=2)
g1.add_edge(0, 1, w=1.0, spectra=[0.5, 0.2])
g2 = nx.Graph()
g2.add_node(0, category=(1, 3), symbol=1)
g2.add_node(1, category=(2, 3, 5), symbol=2)
g2.add_node(2, category=(1, ), symbol=1)
g2.add_edge(0, 1, w=2.0, spectra=[0.1, 0.9, 1.5])
g2.add_edge(0, 2, w=0.5, spectra=[0.4])
g2.add_edge(1, 2, w=0.5, spectra=[0.3, 0.6])
# Define node and edge base kernels using the R-convolution framework
# Reference: Haussler, David. Convolution kernels on discrete structures. 1999.
knode = TensorProduct(symbol=KroneckerDelta(0.5),
category=Convolution(KroneckerDelta(0.5)))
kedge = TensorProduct(spectra=Convolution(SquareExponential(0.3)))
# compose the marginalized graph kernel and compute pairwise similarity
mlgk = MarginalizedGraphKernel(knode, kedge, q=0.05)
R = mlgk([Graph.from_networkx(g, weight='w') for g in [g1, g2]])
# normalize the similarity matrix
d = np.diag(R)**-0.5
K = np.diag(d).dot(R).dot(np.diag(d))
print(K)
weighted_graph1 = nx.Graph(title='H2O')
weighted_graph1.add_node('O1', hybridization=Hybrid.SP2, charge=1)
weighted_graph1.add_node('H1', hybridization=Hybrid.SP3, charge=-1)
weighted_graph1.add_node('H2', hybridization=Hybrid.SP, charge=2)
weighted_graph1.add_edge('O1', 'H1', order=1, length=0.5, w=1.0)
weighted_graph1.add_edge('O1', 'H2', order=2, length=1.0, w=2.0)
weighted_graph2 = nx.Graph(title='H2')
weighted_graph2.add_node('H1', hybridization=Hybrid.SP, charge=1)
weighted_graph2.add_node('H2', hybridization=Hybrid.SP, charge=1)
weighted_graph2.add_edge('H1', 'H2', order=2, length=1.0, w=3.0)
case_dict = {
'unlabeled': {
'graphs': [
Graph.from_networkx(unlabeled_graph1),
Graph.from_networkx(unlabeled_graph2)
],
'knode':
Constant(1.0),
'kedge':
Constant(1.0),
'q': [0.01, 0.05, 0.1, 0.5]
},
'labeled': {
'graphs': [
Graph.from_networkx(labeled_graph1),
Graph.from_networkx(labeled_graph2)
],
'knode':
TensorProduct(hybridization=KroneckerDelta(0.3, 1.0),