def parse_input(self, X):
"""Parse input and create features, while initializing and/or calculating sub-kernels.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
base_graph_kernel : object
Returns base_graph_kernel. Only if called from `fit` or `fit_transform`.
K : np.array
Returns the kernel matrix. Only if called from `transform` or
`fit_transform`.
"""
# Input validation and parsing
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
nx, max_core_number, core_numbers, graphs = 0, 0, [], []
for (idx, x) in enumerate(iter(X)):
is_iter = False
extra = tuple()
if isinstance(x, collections.Iterable):
x, is_iter = list(x), True
if is_iter and len(x) >= 0:
if len(x) == 0:
warnings.warn('Ignoring empty element on index: ' +
str(idx))
continue
elif len(x) == 1:
x = Graph(x[0], {}, {}, graph_format="adjacency")
elif len(x) == 2:
x = Graph(x[0], x[1], {}, graph_format="adjacency")
elif len(x) >= 3:
if len(x) > 3:
extra += tuple(x[3:])
x = Graph(x[0], x[1], x[2], graph_format="adjacency")
elif type(x) is Graph:
x.desired_format("adjacency")
x = Graph(
x.get_adjacency_matrix(),
x.get_labels(purpose="adjacency",
label_type="vertex",
return_none=True),
x.get_labels(purpose="adjacency",
label_type="edge",
return_none=True))
else:
raise TypeError('each element of X must be either a '
'graph object or a list with at least '
'a graph like object and node labels '
'dict \n')
# workaround for leaving a sparse representation for x
x.change_format(self._graph_format)
c = core_number(x)
max_core_number = max(max_core_number, max(c.values()))
core_numbers.append(c)
graphs.append((x, extra))
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
if max_core_number <= self.min_core:
raise ValueError(
'The maximum core equals the min_core boundary set in init.')
# Add the zero iteration element
if self._method_calling == 2:
K = np.zeros(shape=(nx, nx))
elif self._method_calling == 3:
self._dummy_kernel = dict()
K = np.zeros(shape=(nx, self._nx))
# Main
base_graph_kernel, indexes_list = dict(), dict()
for i in range(max_core_number, self.min_core, -1):
subgraphs, indexes = list(), list()
for (idx, (cn, (g, extra))) in enumerate(zip(core_numbers,
graphs)):
vertices = [k for k, v in iteritems(cn) if v >= i]
if len(vertices) > 0:
# Calculate subgraph and store the index of the non-empty vertices
sg = g.get_subgraph(vertices)
sub_extra = list()
indexes.append(idx)
if len(extra) > 0:
vs = np.array(sg.get_vertices(purpose='any'))
for e in extra:
# This case will only be reached by now if the user add the propagation
# kernel as subkernel with a custom propagation matrix. This is a workaround!
if type(e) is np.array and len(e.shape) == 2:
e = e[vs, :][:, vs]
sub_extra.append(e)
subgraphs.append((sg, ) + tuple(sub_extra))
else:
subgraphs.append(sg)
indexes = np.array(indexes)
indexes_list[i] = indexes
# calculate kernel
if self._method_calling == 1 and indexes.shape[0] > 0:
base_graph_kernel[i] = self.base_graph_kernel_(**self.params_)
base_graph_kernel[i].fit(subgraphs)
elif self._method_calling == 2 and indexes.shape[0] > 0:
base_graph_kernel[i] = self.base_graph_kernel_(**self.params_)
ft_subgraph_mat = base_graph_kernel[i].fit_transform(subgraphs)
for j in range(indexes.shape[0]):
K[indexes[j], indexes] += ft_subgraph_mat[j, :]
elif self._method_calling == 3:
if self._max_core_number < i or self._fit_indexes[i].shape[
0] == 0:
if len(indexes) > 0:
# add a dummy kernel for calculating the diagonal
self._dummy_kernel[i] = self.base_graph_kernel_(
**self.params_)
self._dummy_kernel[i].fit(subgraphs)
else:
if indexes.shape[0] > 0:
subgraph_tmat = self.X[i].transform(subgraphs)
for j in range(indexes.shape[0]):
K[indexes[j],
self._fit_indexes[i]] += subgraph_tmat[j, :]
if self._method_calling == 1:
self._nx = nx
self._max_core_number = max_core_number
self._fit_indexes = indexes_list
return base_graph_kernel
elif self._method_calling == 2:
self._nx = nx
self._max_core_number = max_core_number
self._fit_indexes = indexes_list
return K, base_graph_kernel
elif self._method_calling == 3:
self._t_nx = nx
self._max_core_number_trans = max_core_number
self._transform_indexes = indexes_list
return K
def parse_input(self, X):
"""Parse and create features for graphlet_sampling kernel.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
out : list
The extracted adjacency matrices for any given input.
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
i = 0
proc = list()
for (idx, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and len(x) in [1, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element' +
' on index: ' + str(idx))
continue
else:
x = Graph(x[0], x[1], {}, self._graph_format)
elif type(x) is not Graph:
raise TypeError('each element of X must be either a ' +
'graph or an iterable with at least 2 ' +
'and at most 3 elements\n')
i += 1
x.desired_format("adjacency")
Ax = x.get_adjacency_matrix()
Lx = x.get_labels(purpose="adjacency")
Lx = [Lx[idx] for idx in range(Ax.shape[0])]
proc.append((Ax, Lx, Ax.shape[0]))
out = list()
for Ax, Lx, s in proc:
amss = dict()
labels = set(Lx)
Lx = np.array(Lx)
for t in product(labels, labels):
selector = np.matmul(np.expand_dims(Lx == t[0], axis=1),
np.expand_dims(Lx == t[1], axis=0))
amss[t] = Ax * selector
out.append((amss, s))
if i == 0:
raise ValueError('parsed input is empty')
return out
def parse_input(self, X):
"""Parse input for weisfeiler lehman.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
base_kernel : object
Returns base_kernel.
"""
if self._method_calling not in [1, 2]:
raise ValueError('method call must be called either from fit ' +
'or fit-transform')
elif hasattr(self, '_X_diag'):
# Clean _X_diag value
delattr(self, '_X_diag')
# Input validation and parsing
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
nx = 0
Gs_ed, L, distinct_values, extras = dict(), dict(), set(), dict()
for (idx, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and (len(x) == 0 or len(x) >= 2):
if len(x) == 0:
warnings.warn('Ignoring empty element on index: ' +
str(idx))
continue
else:
if len(x) > 2:
extra = tuple()
if len(x) > 3:
extra = tuple(x[3:])
x = Graph(x[0],
x[1],
x[2],
graph_format=self._graph_format)
extra = (x.get_labels(purpose=self._graph_format,
label_type="edge",
return_none=True), ) + extra
else:
x = Graph(x[0],
x[1], {},
graph_format=self._graph_format)
extra = tuple()
elif type(x) is Graph:
x.desired_format(self._graph_format)
el = x.get_labels(purpose=self._graph_format,
label_type="edge",
return_none=True)
if el is None:
extra = tuple()
else:
extra = (el, )
else:
raise TypeError('each element of X must be either a ' +
'graph object or a list with at least ' +
'a graph like object and node labels ' +
'dict \n')
Gs_ed[nx] = x.get_edge_dictionary()
L[nx] = x.get_labels(purpose="dictionary")
extras[nx] = extra
distinct_values |= set(itervalues(L[nx]))
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
# Save the number of "fitted" graphs.
self._nx = nx
# get all the distinct values of current labels
WL_labels_inverse = dict()
# assign a number to each label
label_count = 0
for dv in sorted(list(distinct_values)):
WL_labels_inverse[dv] = label_count
label_count += 1
# Initalize an inverse dictionary of labels for all iterations
self._inv_labels = dict()
self._inv_labels[0] = WL_labels_inverse
def generate_graphs(label_count, WL_labels_inverse):
new_graphs = list()
for j in range(nx):
new_labels = dict()
for k in L[j].keys():
new_labels[k] = WL_labels_inverse[L[j][k]]
L[j] = new_labels
# add new labels
new_graphs.append((Gs_ed[j], new_labels) + extras[j])
yield new_graphs
for i in range(1, self._n_iter):
label_set, WL_labels_inverse, L_temp = set(), dict(), dict()
for j in range(nx):
# Find unique labels and sort
# them for both graphs
# Keep for each node the temporary
L_temp[j] = dict()
for v in Gs_ed[j].keys():
credential = str(L[j][v]) + "," + \
str(sorted([L[j][n] for n in Gs_ed[j][v].keys()]))
L_temp[j][v] = credential
label_set.add(credential)
label_list = sorted(list(label_set))
for dv in label_list:
WL_labels_inverse[dv] = label_count
label_count += 1
# Recalculate labels
new_graphs = list()
for j in range(nx):
new_labels = dict()
for k in L_temp[j].keys():
new_labels[k] = WL_labels_inverse[L_temp[j][k]]
L[j] = new_labels
# relabel
new_graphs.append((Gs_ed[j], new_labels) + extras[j])
self._inv_labels[i] = WL_labels_inverse
yield new_graphs
base_kernel = {
i: self._base_kernel(**self._params)
for i in range(self._n_iter)
}
if self._parallel is None:
if self._method_calling == 1:
for (i, g) in enumerate(
generate_graphs(label_count, WL_labels_inverse)):
base_kernel[i].fit(g)
elif self._method_calling == 2:
K = np.sum(
(base_kernel[i].fit_transform(g) for (i, g) in enumerate(
generate_graphs(label_count, WL_labels_inverse))),
axis=0)
else:
if self._method_calling == 1:
self._parallel(
joblib.delayed(efit)(base_kernel[i], g)
for (i, g) in enumerate(
generate_graphs(label_count, WL_labels_inverse)))
elif self._method_calling == 2:
K = np.sum(self._parallel(
joblib.delayed(efit_transform)(base_kernel[i], g)
for (i, g) in enumerate(
generate_graphs(label_count, WL_labels_inverse))),
axis=0)
if self._method_calling == 1:
return base_kernel
elif self._method_calling == 2:
return K, base_kernel
def transform(self, X):
"""Calculate the kernel matrix, between given and fitted dataset.
Parameters
----------
X : iterable
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that fitting the given graph
format). If None the kernel matrix is calculated upon fit data.
The test samples.
Returns
-------
K : numpy array, shape = [n_targets, n_input_graphs]
corresponding to the kernel matrix, a calculation between
all pairs of graphs between target an features
"""
self._method_calling = 3
# Check is fit had been called
check_is_fitted(self, ['X', '_nx', '_inv_labels'])
# Input validation and parsing
if X is None:
raise ValueError('transform input cannot be None')
else:
if not isinstance(X, collections.Iterable):
raise ValueError('input must be an iterable\n')
else:
nx = 0
distinct_values = set()
Gs_ed, L = dict(), dict()
for (i, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and len(x) in [0, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element on index: ' +
str(i))
continue
elif len(x) in [2, 3]:
x = Graph(x[0], x[1], {}, self._graph_format)
elif type(x) is Graph:
x.desired_format("dictionary")
else:
raise ValueError('each element of X must have at ' +
'least one and at most 3 elements\n')
Gs_ed[nx] = x.get_edge_dictionary()
L[nx] = x.get_labels(purpose="dictionary")
# Hold all the distinct values
distinct_values |= set(v for v in itervalues(L[nx])
if v not in self._inv_labels[0])
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
nl = len(self._inv_labels[0])
WL_labels_inverse = {
dv: idx
for (idx, dv) in enumerate(sorted(list(distinct_values)), nl)
}
def generate_graphs(WL_labels_inverse, nl):
# calculate the kernel matrix for the 0 iteration
new_graphs = list()
for j in range(nx):
new_labels = dict()
for (k, v) in iteritems(L[j]):
if v in self._inv_labels[0]:
new_labels[k] = self._inv_labels[0][v]
else:
new_labels[k] = WL_labels_inverse[v]
L[j] = new_labels
# produce the new graphs
new_graphs.append([Gs_ed[j], new_labels])
yield new_graphs
for i in range(1, self._n_iter):
new_graphs = list()
L_temp, label_set = dict(), set()
nl += len(self._inv_labels[i])
for j in range(nx):
# Find unique labels and sort them for both graphs
# Keep for each node the temporary
L_temp[j] = dict()
for v in Gs_ed[j].keys():
credential = str(L[j][v]) + "," + \
str(sorted([L[j][n] for n in Gs_ed[j][v].keys()]))
L_temp[j][v] = credential
if credential not in self._inv_labels[i]:
label_set.add(credential)
# Calculate the new label_set
WL_labels_inverse = dict()
if len(label_set) > 0:
for dv in sorted(list(label_set)):
idx = len(WL_labels_inverse) + nl
WL_labels_inverse[dv] = idx
# Recalculate labels
new_graphs = list()
for j in range(nx):
new_labels = dict()
for (k, v) in iteritems(L_temp[j]):
if v in self._inv_labels[i]:
new_labels[k] = self._inv_labels[i][v]
else:
new_labels[k] = WL_labels_inverse[v]
L[j] = new_labels
# Create the new graphs with the new labels.
new_graphs.append([Gs_ed[j], new_labels])
yield new_graphs
if self._parallel is None:
# Calculate the kernel matrix without parallelization
K = np.sum(
(self.X[i].transform(g)
for (i,
g) in enumerate(generate_graphs(WL_labels_inverse, nl))),
axis=0)
else:
# Calculate the kernel marix with parallelization
K = np.sum(self._parallel(
joblib.delayed(etransform)(self.X[i], g)
for (i,
g) in enumerate(generate_graphs(WL_labels_inverse, nl))),
axis=0)
self._is_transformed = True
if self.normalize:
X_diag, Y_diag = self.diagonal()
old_settings = np.seterr(divide='ignore')
K = np.nan_to_num(np.divide(K, np.sqrt(np.outer(Y_diag, X_diag))))
np.seterr(**old_settings)
return K
def parse_input(
self,
X,
):
"""Parse input for weisfeiler lehman.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
return_embedding_only: bool
Whether to return the embedding of the graphs only, instead of computing the kernel all
the way to the end.
Returns
-------
base_graph_kernel : object
Returns base_graph_kernel.
"""
if self._method_calling not in [1, 2]:
raise ValueError('method call must be called either from fit ' +
'or fit-transform')
elif hasattr(self, '_X_diag'):
# Clean _X_diag value
delattr(self, '_X_diag')
# Input validation and parsing
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
nx = 0
Gs_ed, L, distinct_values, extras = dict(), dict(), set(), dict()
for (idx, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and (len(x) == 0 or len(x) >= 2):
if len(x) == 0:
warnings.warn('Ignoring empty element on index: ' +
str(idx))
continue
else:
if len(x) > 2:
extra = tuple()
if len(x) > 3:
extra = tuple(x[3:])
x = Graph(x[0],
x[1],
x[2],
graph_format=self._graph_format)
extra = (x.get_labels(purpose=self._graph_format,
label_type="edge",
return_none=True), ) + extra
else:
x = Graph(x[0],
x[1], {},
graph_format=self._graph_format)
extra = tuple()
elif type(x) is Graph:
x.desired_format(self._graph_format)
el = x.get_labels(purpose=self._graph_format,
label_type="edge",
return_none=True)
if el is None:
extra = tuple()
else:
extra = (el, )
else:
raise TypeError('each element of X must be either a ' +
'graph object or a list with at least ' +
'a graph like object and node labels ' +
'dict \n')
Gs_ed[nx] = x.get_edge_dictionary()
L[nx] = x.get_labels(purpose="dictionary")
extras[nx] = extra
distinct_values |= set(itervalues(L[nx]))
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
# Save the number of "fitted" graphs.
self._nx = nx
WL_labels_inverse = OrderedDict()
# assign a number to each label
label_count = 0
for dv in sorted(list(distinct_values)):
WL_labels_inverse[dv] = label_count
label_count += 1
# Initalize an inverse dictionary of labels for all iterations
self._inv_labels = OrderedDict(
) # Inverse dictionary of labels, in term of the *previous layer*
self._inv_labels[0] = deepcopy(WL_labels_inverse)
self.feature_dims.append(
len(WL_labels_inverse)) # Update the zeroth iteration feature dim
# self._inv_label_node_attr = OrderedDict() # Inverse dictionary of labels, in term of the *node attribute*
# self._label_node_attr = OrderedDict() # Same as above, but with key and value inverted
# self._label_node_attr[0], self._inv_label_node_attr[0] = self.translate_label(WL_labels_inverse, 0)
# if self.node_weights is not None:
# self._feature_weight = OrderedDict()
# # Ensure the order is the same
# self._feature_weight[0] = self._compute_feature_weight(self.node_weights, 0, WL_labels_inverse)[1]
# else:
# self._feature_weight = None
def generate_graphs(label_count, WL_labels_inverse):
new_graphs = list()
for j in range(self._nx):
new_labels = dict()
for k in L[j].keys():
new_labels[k] = WL_labels_inverse[L[j][k]]
L[j] = new_labels
# add new labels
new_graphs.append((Gs_ed[j], new_labels) + extras[j])
yield new_graphs
for i in range(1, self._h):
label_set, WL_labels_inverse, L_temp = set(), dict(), dict()
for j in range(nx):
# Find unique labels and sort
# them for both graphs
# Keep for each node the temporary
L_temp[j] = dict()
for v in Gs_ed[j].keys():
credential = str(L[j][v]) + "," + \
str(sorted([L[j][n] for n in Gs_ed[j][v].keys()]))
L_temp[j][v] = credential
label_set.add(credential)
label_list = sorted(list(label_set))
for dv in label_list:
WL_labels_inverse[dv] = label_count
label_count += 1
# Recalculate labels
new_graphs = list()
for j in range(nx):
new_labels = dict()
for k in L_temp[j].keys():
new_labels[k] = WL_labels_inverse[L_temp[j][k]]
L[j] = new_labels
# relabel
new_graphs.append((Gs_ed[j], new_labels) + extras[j])
self._inv_labels[i] = WL_labels_inverse
# Compute the translated inverse node label
# self._label_node_attr[i], self._inv_label_node_attr[i] = self.translate_label(WL_labels_inverse, i, self._label_node_attr[i - 1])
# self.feature_dims.append(self.feature_dims[-1] + len(self._label_node_attr[i]))
# Compute the feature weight of the current layer
# if self.node_weights is not None:
# self._feature_weight[i] = self._compute_feature_weight(self.node_weights, i, self._inv_label_node_attr[i])[1]
# assert len(self._feature_weight[i] == len(WL_labels_inverse))
yield new_graphs
# Initialise the base graph kernel.
base_graph_kernel = {}
K = []
for (i, g) in enumerate(generate_graphs(label_count,
WL_labels_inverse)):
param = self._params
# if self._feature_weight is not None:
# print(self._feature_weight)
# param.update({'mahalanobis_precision': self._feature_weight[i]})
base_graph_kernel.update({i: self._base_graph_kernel(**param)})
# if return_embedding_only:
# K.append(base_graph_kernel[i].parse_input(
# g, label_start_idx=self.feature_dims[i], label_end_idx=self.feature_dims[i + 1]))
# else:
if self._method_calling == 1:
base_graph_kernel[i].fit(g, )
else:
K.append(base_graph_kernel[i].fit_transform(g, ))
# if return_embedding_only:
# return K
if self._method_calling == 1:
return base_graph_kernel
elif self._method_calling == 2:
# if self.as_tensor:
# K = torch.stack(K, dim=0).sum(dim=0)
# return K, base_graph_kernel
return np.sum(K, axis=0), base_graph_kernel
def parse_input(self, X):
"""Fast ML Graph Kernel.
See supplementary material :cite:`kondor2016multiscale`, algorithm 1.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
out : list
A list of tuples with S matrices inverses
and their 4th-root determinants.
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
ng = 0
out = list()
data = dict()
neighborhoods = dict()
for (idx, x) in enumerate(iter(X)):
is_iter = False
if isinstance(x, collections.Iterable):
is_iter, x = True, list(x)
if is_iter and len(x) in [0, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element ' +
'on index: ' + str(idx))
continue
else:
x = Graph(x[0], x[1], {}, self._graph_format)
elif type(x) is Graph:
x.desired_format(self._graph_format)
else:
raise TypeError('each element of X must be either a '
'graph or an iterable with at least 1 '
'and at most 3 elements\n')
phi_d = x.get_labels()
A = x.get_adjacency_matrix()
try:
phi = np.array([list(phi_d[i]) for i in range(A.shape[0])])
except TypeError:
raise TypeError('Features must be iterable and castable '
'in total to a numpy array.')
Lap = laplacian(A).astype(float)
_increment_diagonal_(Lap, self.heta)
data[ng] = {0: A, 1: phi, 2: inv(Lap)}
neighborhoods[ng] = x
ng += 1
if ng == 0:
raise ValueError('parsed input is empty')
# Define a function for calculating the S's of subgraphs of each iteration
def calculate_C(k, j, l):
if type(neighborhoods[k]) is Graph:
neighborhoods[k] = neighborhoods[k].produce_neighborhoods(
r=self.L, sort_neighbors=False)
indexes = neighborhoods[k][l][j]
L = laplacian(data[k][0][indexes, :][:, indexes]).astype(float)
_increment_diagonal_(L, self.heta)
U = data[k][1][indexes, :]
S = multi_dot((U.T, inv(L), U))
_increment_diagonal_(S, self.gamma)
return (inv(S), np.sum(np.log(np.real(eigvals(S)))))
if self._method_calling == 1:
V = [(k, j) for k in range(ng)
for j in range(data[k][0].shape[0])]
ns = min(len(V), self.n_samples)
self.random_state_.shuffle(V)
vs = V[:ns]
phi_k = np.array([data[k][1][j, :] for (k, j) in vs])
# w the eigen vectors, v the eigenvalues
K = phi_k.dot(phi_k.T)
# Calculate eigenvalues
v, w = eig(K)
v, w = np.real(v), np.real(w.T)
# keep only the positive
vpos = np.argpartition(v, -self.P)[-self.P:]
vpos = vpos[np.where(v[vpos] > positive_eigenvalue_limit)]
# ksi.shape = (k, Ns) * (Ns, P)
ksi = w[vpos].dot(phi_k).T / np.sqrt(v[vpos])
for j in range(ng):
# (n_samples, k) * (k, P)
data[j][1] = data[j][1].dot(ksi)
self._data_level = {0: ksi}
for l in range(1, self.L + 1):
# Take random samples from all the vertices of all graphs
self.random_state_.shuffle(V)
vs = V[:ns]
# Compute the reference subsampled Gram matrix
K_proj = {
k: np.zeros(shape=(data[k][0].shape[0], ns))
for k in range(ng)
}
K, C = np.zeros(shape=(len(vs), len(vs))), dict()
for (m, (k, j)) in enumerate(vs):
C[m] = calculate_C(k, j, l)
K_proj[k][j, m] = K[m, m] = self.pairwise_operation(
C[m], C[m])
for (s, (k2, j2)) in enumerate(vs):
if s < m:
K[s, m] = K[m, s] \
= K_proj[k2][j2, m] \
= K_proj[k][j, s] \
= self.pairwise_operation(C[s], C[m])
else:
break
# Compute the kernels of the relations of the reference to everything else
for (k, j) in V[ns:]:
for (m, _) in enumerate(vs):
K_proj[k][j, m] = self.pairwise_operation(
C[m], calculate_C(k, j, l))
# w the eigen vectors, v the eigenvalues
v, w = eig(K)
v, w = np.real(v), np.real(w.T)
# keep only the positive
vpos = np.argpartition(v, -self.P)[-self.P:]
vpos = vpos[np.where(v[vpos] > positive_eigenvalue_limit)]
# Q shape=(k, P)
Q = w[vpos].T / np.sqrt(v[vpos])
for j in range(ng):
# (n, ns) * (ns, P)
data[j][1] = K_proj[j].dot(Q)
self._data_level[l] = (C, Q)
elif self._method_calling == 3:
ksi = self._data_level[0]
for j in range(ng):
# (n, k) * (k, P)
data[j][1] = data[j][1].dot(ksi)
for l in range(1, self.L + 1):
C, Q = self._data_level[l]
for j in range(ng):
K_proj = np.zeros(shape=(data[j][0].shape[0], len(C)))
for n in range(data[j][0].shape[0]):
for m in range(len(C)):
K_proj[n, m] = self.pairwise_operation(
C[m], calculate_C(j, n, l))
data[j][1] = K_proj.dot(Q)
# Apply the final calculation of S.
for k in range(ng):
S = multi_dot((data[k][1].T, data[k][2], data[k][1]))
_increment_diagonal_(S, self.gamma)
out.append((inv(S), np.sum(np.log(np.real(eigvals(S))))))
return out
def parse_input(self, X):
"""Parse and create features for multiscale_laplacian kernel.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
out : list
Tuples consisting of the Adjacency matrix, phi, phi_outer
dictionary of neihborhood indexes and inverse laplacians
up to level self.L and the inverse Laplacian of A.
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
ng = 0
out = list()
start = time.time()
for (idx, x) in enumerate(iter(X)):
is_iter = False
if isinstance(x, collections.Iterable):
is_iter, x = True, list(x)
if is_iter and len(x) in [0, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element ' +
'on index: ' + str(idx))
continue
else:
x = Graph(x[0], x[1], {}, self._graph_format)
elif type(x) is not Graph:
x.desired_format(self._graph_format)
else:
raise TypeError('each element of X must be either a ' +
'graph or an iterable with at least 1 ' +
'and at most 3 elements\n')
ng += 1
phi_d = x.get_labels()
A = x.get_adjacency_matrix()
N = x.produce_neighborhoods(r=self.L, sort_neighbors=False)
try:
phi = np.array([list(phi_d[i]) for i in range(A.shape[0])])
except TypeError:
raise TypeError('Features must be iterable and castable ' +
'in total to a numpy array.')
phi_outer = np.dot(phi, phi.T)
Lap = laplacian(A).astype(float)
_increment_diagonal_(Lap, self.heta)
L = inv(Lap)
Q = dict()
for level in range(1, self.L + 1):
Q[level] = dict()
for (key, item) in iteritems(N[level]):
Q[level][key] = dict()
Q[level][key]["n"] = np.array(item)
if len(item) < A.shape[0]:
laplac = laplacian(A[item, :][:,
item]).astype(float)
_increment_diagonal_(laplac, self.heta)
laplac = inv(laplac)
else:
laplac = L
Q[level][key]["l"] = laplac
out.append((A, phi, phi_outer, Q, L))
if self.verbose:
print("Preprocessing took:", time.time() - start, "s.")
if ng == 0:
raise ValueError('parsed input is empty')
return out
def parse_input(self, X):
"""Parse input for weisfeiler lehman optimal assignment.
Parameters
----------
X : iterable
For the input to pass the test, we must have:
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that correspond to the given
graph format). A valid input also consists of graph type objects.
Returns
-------
Hs : numpy array, shape = [n_input_graphs, hierarchy_size]
An array where the rows contain the histograms of the graphs.
"""
if self._method_calling not in [1, 2]:
raise ValueError('method call must be called either from fit ' +
'or fit-transform')
elif hasattr(self, '_X_diag'):
# Clean _X_diag value
delattr(self, '_X_diag')
# Input validation and parsing
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
nx = 0
Gs_ed, L, distinct_values = dict(), dict(), set()
for (idx, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and (len(x) == 0 or len(x) >= 2):
if len(x) == 0:
warnings.warn('Ignoring empty element on index: '
+ str(idx))
continue
else:
if len(x) > 2:
extra = tuple()
if len(x) > 3:
extra = tuple(x[3:])
x = Graph(x[0], x[1], x[2], graph_format=self._graph_format)
extra = (x.get_labels(purpose=self._graph_format,
label_type="edge", return_none=True), ) + extra
else:
x = Graph(x[0], x[1], {}, graph_format=self._graph_format)
extra = tuple()
elif type(x) is Graph:
x.desired_format(self._graph_format)
else:
raise TypeError('each element of X must be either a ' +
'graph object or a list with at least ' +
'a graph like object and node labels ' +
'dict \n')
Gs_ed[nx] = x.get_edge_dictionary()
L[nx] = x.get_labels(purpose="dictionary")
distinct_values |= set(itervalues(L[nx]))
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
# Save the number of "fitted" graphs.
self._nx = nx
# Initialize hierarchy
self._hierarchy = dict()
self._hierarchy['root'] = dict()
self._hierarchy['root']['parent'] = None
self._hierarchy['root']['children'] = list()
self._hierarchy['root']['w'] = 0
self._hierarchy['root']['omega'] = 0
# get all the distinct values of current labels
WL_labels_inverse = dict()
# assign a number to each label
label_count = 0
for dv in sorted(list(distinct_values)):
WL_labels_inverse[dv] = label_count
self._insert_into_hierarchy(label_count, 'root')
label_count += 1
# Initalize an inverse dictionary of labels for all iterations
self._inv_labels = dict()
self._inv_labels[0] = WL_labels_inverse
for j in range(nx):
new_labels = dict()
for k in L[j].keys():
new_labels[k] = WL_labels_inverse[L[j][k]]
L[j] = new_labels
for i in range(1, self._n_iter):
new_previous_label_set, WL_labels_inverse, L_temp = set(), dict(), dict()
for j in range(nx):
# Find unique labels and sort
# them for both graphs
# Keep for each node the temporary
L_temp[j] = dict()
for v in Gs_ed[j].keys():
credential = str(L[j][v]) + "," + \
str(sorted([L[j][n] for n in Gs_ed[j][v].keys()]))
L_temp[j][v] = credential
new_previous_label_set.add((credential, L[j][v]))
label_list = sorted(list(new_previous_label_set), key=lambda tup: tup[0])
for dv, previous_label in label_list:
WL_labels_inverse[dv] = label_count
self._insert_into_hierarchy(label_count, previous_label)
label_count += 1
# Recalculate labels
for j in range(nx):
new_labels = dict()
for k in L_temp[j].keys():
new_labels[k] = WL_labels_inverse[L_temp[j][k]]
L[j] = new_labels
self._inv_labels[i] = WL_labels_inverse
# Compute the vector representation of each graph
if self.sparse:
Hs = lil_matrix((nx, len(self._hierarchy)))
else:
Hs = np.zeros((nx, len(self._hierarchy)))
for j in range(nx):
for k in L[j].keys():
current_label = L[j][k]
while self._hierarchy[current_label]['parent'] is not None:
Hs[j, current_label] += self._hierarchy[current_label]['omega']
current_label = self._hierarchy[current_label]['parent']
return Hs
def transform(self, X):
"""Calculate the kernel matrix, between given and fitted dataset.
Parameters
----------
X : iterable
Each element must be an iterable with at most three features and at
least one. The first that is obligatory is a valid graph structure
(adjacency matrix or edge_dictionary) while the second is
node_labels and the third edge_labels (that fitting the given graph
format). If None the kernel matrix is calculated upon fit data.
The test samples.
Returns
-------
K : numpy array, shape = [n_targets, n_input_graphs]
corresponding to the kernel matrix, a calculation between
all pairs of graphs between target an features
"""
self._method_calling = 3
# Check is fit had been called
check_is_fitted(self, ['X', '_nx', '_hierarchy', '_inv_labels'])
# Input validation and parsing
if X is None:
raise ValueError('transform input cannot be None')
else:
if not isinstance(X, collections.Iterable):
raise ValueError('input must be an iterable\n')
else:
nx = 0
distinct_values = set()
Gs_ed, L = dict(), dict()
for (i, x) in enumerate(iter(X)):
is_iter = isinstance(x, collections.Iterable)
if is_iter:
x = list(x)
if is_iter and len(x) in [0, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element on index: '
+ str(i))
continue
elif len(x) in [2, 3]:
x = Graph(x[0], x[1], {}, self._graph_format)
elif type(x) is Graph:
x.desired_format("dictionary")
else:
raise ValueError('each element of X must have at ' +
'least one and at most 3 elements\n')
Gs_ed[nx] = x.get_edge_dictionary()
L[nx] = x.get_labels(purpose="dictionary")
# Hold all the distinct values
distinct_values |= set(
v for v in itervalues(L[nx])
if v not in self._inv_labels[0])
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
# get all the distinct values of new labels
WL_labels_inverse = dict()
# assign a number to each label
label_count = sum([len(self._inv_labels[i]) for i in range(len(self._inv_labels))])
for dv in sorted(list(distinct_values)):
WL_labels_inverse[dv] = label_count
self._insert_into_hierarchy(label_count, 'root')
label_count += 1
for j in range(nx):
new_labels = dict()
for (k, v) in iteritems(L[j]):
if v in self._inv_labels[0]:
new_labels[k] = self._inv_labels[0][v]
else:
new_labels[k] = WL_labels_inverse[v]
L[j] = new_labels
for i in range(1, self._n_iter):
L_temp, new_previous_label_set = dict(), set()
for j in range(nx):
# Find unique labels and sort them for both graphs
# Keep for each node the temporary
L_temp[j] = dict()
for v in Gs_ed[j].keys():
credential = str(L[j][v]) + "," + \
str(sorted([L[j][n] for n in Gs_ed[j][v].keys()]))
L_temp[j][v] = credential
if credential not in self._inv_labels[i]:
new_previous_label_set.add((credential, L[j][v]))
# Calculate the new label_set
WL_labels_inverse = dict()
if len(new_previous_label_set) > 0:
for dv, previous_label in sorted(list(new_previous_label_set), key=lambda tup: tup[0]):
WL_labels_inverse[dv] = label_count
self._insert_into_hierarchy(label_count, previous_label)
label_count += 1
# Recalculate labels
for j in range(nx):
new_labels = dict()
for (k, v) in iteritems(L_temp[j]):
if v in self._inv_labels[i]:
new_labels[k] = self._inv_labels[i][v]
else:
new_labels[k] = WL_labels_inverse[v]
L[j] = new_labels
# Compute the vector representation of each graph
if self.sparse:
Hs = lil_matrix((nx, len(self._hierarchy)))
else:
Hs = np.zeros((nx, len(self._hierarchy)))
for j in range(nx):
for k in L[j].keys():
current_label = L[j][k]
while self._hierarchy[current_label]['parent'] is not None:
Hs[j, current_label] += self._hierarchy[current_label]['omega']
current_label = self._hierarchy[current_label]['parent']
self.Y = Hs
# Compute the histogram intersection kernel
K = np.zeros((nx, self._nx))
if self.sparse:
for i in range(self._nx):
for j in range(i, self._nx):
K[i, j] = np.sum(Hs[i, :self.X.shape[1]].minimum(self.X[j, :]))
else:
for i in range(nx):
for j in range(self._nx):
K[i, j] = np.sum(np.min([Hs[i, :self.X.shape[1]], self.X[j, :]], axis=0))
self._is_transformed = True
if self.normalize:
X_diag, Y_diag = self.diagonal()
old_settings = np.seterr(divide='ignore')
K = np.nan_to_num(np.divide(K, np.sqrt(np.outer(Y_diag, X_diag))))
np.seterr(**old_settings)
return K