def fit(self, X, y=None):
"""Fit a dataset, for a transformer.
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). The train samples.
y : None
There is no need of a target in a transformer, yet the pipeline API
requires this parameter.
Returns
-------
self : object
Returns self.
"""
self._method_calling = 1
self._is_transformed = False
# Input validation and parsing
self.initialize()
if X is None:
raise ValueError('`fit` input cannot be None')
else:
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
i = 0
out = list()
gs = list()
self._labels_hash_dict, labels_hash_set = 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) in [0, 1, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element on index: '
+ str(idx))
continue
elif len(x) == 1:
warnings.warn(
'Ignoring empty element on index: '
+ str(i) + '\nLabels must be provided.')
else:
x = Graph(x[0], x[1], {}, self._graph_format)
vertices = list(x.get_vertices(purpose="any"))
Labels = x.get_labels(purpose="any")
elif type(x) is Graph:
vertices = list(x.get_vertices(purpose="any"))
Labels = x.get_labels(purpose="any")
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')
g = (vertices, Labels,
{n: x.neighbors(n, purpose="any") for n in vertices})
# collect all the labels
labels_hash_set |= set(itervalues(Labels))
gs.append(g)
i += 1
if i == 0:
raise ValueError('parsed input is empty')
# Hash labels
if len(labels_hash_set) > self._max_number:
warnings.warn('Number of labels is smaller than'
'the biggest possible.. '
'Collisions will appear on the '
'new labels.')
# If labels exceed the biggest possible size
nl, nrl = list(), len(labels_hash_set)
while nrl > self._max_number:
nl += self.random_state_.choice(self._max_number,
self._max_number,
replace=False).tolist()
nrl -= self._max_number
if nrl > 0:
nl += self.random_state_.choice(self._max_number,
nrl,
replace=False).tolist()
# unify the collisions per element.
else:
# else draw n random numbers.
nl = self.random_state_.choice(self._max_number, len(labels_hash_set),
replace=False).tolist()
self._labels_hash_dict = dict(zip(labels_hash_set, nl))
# for all graphs
for vertices, labels, neighbors in gs:
new_labels = {v: self._labels_hash_dict[l]
for v, l in iteritems(labels)}
g = (vertices, new_labels, neighbors,)
gr = {0: self.NH_(g)}
for r in range(1, self.R):
gr[r] = self.NH_(gr[r-1])
# save the output for all levels
out.append(gr)
self.X = out
# Return the transformer
return self
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 the attributed propation 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
-------
local_values : dict
A dictionary of pairs between each input graph and a bins where the
sampled graphlets have fallen.
"""
if not isinstance(X, collections.Iterable):
raise ValueError('input must be an iterable\n')
else:
# The number of parsed graphs
n = 0
transition_matrix = dict()
indexes = [0]
Attr = 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 [0, 2, 3, 4]:
if len(x) == 0:
warnings.warn('Ignoring empty element on ' +
'index: ' + str(idx))
continue
if len(x) == 2 and type(x[0]) is Graph:
g, T = x
else:
g = Graph(x[0], x[1], {}, self._graph_format)
if len(x) == 4:
T = x[3]
else:
T = None
elif type(x) is Graph:
g, T = x, None
else:
raise ValueError('Each element of X must be either a ' +
'Graph or an iterable with at least 2 ' +
'and at most 4 elements\n')
if T is not None:
if T.shape[0] != T.shape[1]:
raise TypeError('Transition matrix on index' + ' ' +
str(idx) + 'must be ' +
'a square matrix.')
if T.shape[0] != g.nv():
raise TypeError('Propagation matrix must ' +
'have the same dimension ' +
'as the number of vertices.')
else:
T = g.get_adjacency_matrix()
nv = g.nv()
transition_matrix[n] = (T.T / np.sum(T, axis=1)).T
attr = g.get_labels(purpose="adjacency")
try:
attributes = np.array([attr[j] for j in range(nv)])
except TypeError:
raise TypeError(
'All attributes of a single graph should have the same dimension.'
)
Attr.append(attributes)
indexes.append(indexes[-1] + nv)
n += 1
try:
P = np.vstack(Attr)
except ValueError:
raise ValueError(
'Attribute dimensions should be the same, for all graphs')
if self._method_calling == 1:
self._dim = P.shape[1]
else:
if self._dim != P.shape[1]:
raise ValueError('transform attribute vectors should'
'have the same dimension as in fit')
if n == 0:
raise ValueError('Parsed input is empty')
# feature vectors
if self._method_calling == 1:
# simple normal
self._u, self._b, self._hd = list(), list(), list()
for t in range(self.t_max):
u = self.random_state_.randn(self._dim)
if self.take_cauchy_:
# cauchy
u = np.divide(u, self.random_state_.randn(self._dim))
self._u.append(u)
# random offset
self._b.append(self.w *
self.random_state_.randn(self._dim))
phi = {k: dict() for k in range(n)}
for t in range(self.t_max):
# for hash all graphs inside P and produce the feature vectors
hashes = self.calculate_LSH(P, self._u[t],
self._b[t]).tolist()
hd = {
j: i
for i, j in enumerate({tuple(l)
for l in hashes})
}
self._hd.append(hd)
features = np.array([hd[tuple(l)] for l in hashes])
# Accumulate the results.
for k in range(n):
phi[k][t] = Counter(
features[indexes[k]:indexes[k + 1]].flat)
# calculate the Propagation matrix if needed
if t < self.t_max - 1:
for k in range(n):
start, end = indexes[k:k + 2]
P[start:end, :] = np.dot(transition_matrix[k],
P[start:end, :])
return [phi[k] for k in range(n)]
if self._method_calling == 3:
phi = {k: dict() for k in range(n)}
for t in range(self.t_max):
# for hash all graphs inside P and produce the feature vectors
hashes = self.calculate_LSH(P, self._u[t],
self._b[t]).tolist()
hd = dict(
chain(
iteritems(self._hd[t]),
iter((j, i)
for i, j in enumerate(
filterfalse(lambda x: x in self._hd[t],
{tuple(l)
for l in hashes}),
len(self._hd[t])))))
features = np.array([hd[tuple(l)] for l in hashes])
# Accumulate the results.
for k in range(n):
phi[k][t] = Counter(features[indexes[k]:indexes[k +
1]])
# calculate the Propagation matrix if needed
if t < self.t_max - 1:
for k in range(n):
start, end = indexes[k:k + 2]
P[start:end, :] = np.dot(transition_matrix[k],
P[start:end, :])
return [phi[k] for k in range(n)]
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'])
# Input validation and parsing
if X is None:
raise ValueError('`transform` input cannot be None')
else:
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
i = 0
out = 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 [0, 1, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element on index: '
+ str(idx))
continue
elif len(x) == 1:
warnings.warn(
'Ignoring empty element on index: '
+ str(i) + '\nLabels must be provided.')
else:
x = Graph(x[0], x[1], {}, self._graph_format)
vertices = list(x.get_vertices(purpose="any"))
Labels = x.get_labels(purpose="any")
elif type(x) is Graph:
vertices = list(x.get_vertices(purpose="any"))
Labels = x.get_labels(purpose="any")
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')
# Hash based on the labels of fit
new_labels = {v: self._labels_hash_dict.get(l, None)
for v, l in iteritems(Labels)}
# Radix sort the other
g = ((vertices, new_labels) +
({n: x.neighbors(n, purpose="any")
for n in vertices},))
gr = {0: self.NH_(g)}
for r in range(1, self.R):
gr[r] = self.NH_(gr[r-1])
# save the output for all levels
out.append(gr)
i += 1
if i == 0:
raise ValueError('parsed input is empty')
# Transform - calculate kernel matrix
# Output is always normalized
km = self._calculate_kernel_matrix(out)
self._is_transformed = True
return km
def parse_input(self, X):
"""Parse and create features for pyramid_match 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
-------
H : list
A list of lists of Histograms for all levels for each graph.
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
i = 0
Us = []
if self.with_labels:
Ls = []
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) >= 1 and not self.with_labels) or
(len(x) >= 2 and self.with_labels)):
if len(x) == 0:
warnings.warn('Ignoring empty element on index: ' +
str(idx))
continue
elif not self.with_labels:
x = Graph(x[0], {}, {}, self._graph_format)
else:
x = Graph(x[0], x[1], {}, self._graph_format)
elif not type(x) is Graph:
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')
A = x.get_adjacency_matrix()
if self.with_labels:
L = x.get_labels(purpose="adjacency")
i += 1
if A.shape[0] == 0:
Us.append(np.zeros((1, self.d)))
else:
# Perform eigenvalue decomposition.
# Rows of matrix U correspond to vertex representations
# Embed vertices into the d-dimensional space
if A.shape[0] > self.d + 1:
# If size of graph smaller than d, pad with zeros
Lambda, U = eigs(csr_matrix(A, dtype=np.float),
k=self.d,
ncv=10 * self.d)
idx = Lambda.argsort()[::-1]
U = U[:, idx]
else:
Lambda, U = np.linalg.eig(A)
idx = Lambda.argsort()[::-1]
U = U[:, idx]
U = U[:, :self.d]
# Replace all components by their absolute values
U = np.absolute(U)
Us.append((A.shape[0], U))
if self.with_labels:
Ls.append(L)
if i == 0:
raise ValueError('parsed input is empty')
if self.with_labels:
# Map labels to values between 0 and |L|-1
# where |L| is the number of distinct labels
if self._method_calling in [1, 2]:
self._num_labels = 0
self._labels = set()
for L in Ls:
self._labels |= set(itervalues(L))
self._num_labels = len(self._labels)
self._labels = {l: i for (i, l) in enumerate(self._labels)}
return self._histogram_calculation(Us, Ls, self._labels)
elif self._method_calling == 3:
labels = set()
for L in Ls:
labels |= set(itervalues(L))
rest_labels = labels - set(self._labels.keys())
nouveau_labels = dict(
chain(iteritems(self._labels), ((j, i) for (
i, j) in enumerate(rest_labels, len(self._labels)))))
return self._histogram_calculation(Us, Ls, nouveau_labels)
else:
return self._histogram_calculation(Us)
def parse_input(self, X):
"""Parse and create features for the propation 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
-------
local_values : dict
A dictionary of pairs between each input graph and a bins where the
sampled graphlets have fallen.
"""
if not isinstance(X, collections.Iterable):
raise ValueError('input must be an iterable\n')
else:
i = -1
transition_matrix = dict()
labels = set()
L = 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 [0, 2, 3, 4]:
if len(x) == 0:
warnings.warn('Ignoring empty element on ' +
'index: ' + str(idx))
continue
if len(x) == 2 and type(x[0]) is Graph:
g, T = x
else:
g = Graph(x[0], x[1], {}, self._graph_format)
if len(x) == 4:
T = x[3]
else:
T = None
elif type(x) is Graph:
g, T = x, None
else:
raise ValueError('Each element of X must be either a ' +
'Graph or an iterable with at least 2 ' +
'and at most 4 elements\n')
if T is not None:
if T.shape[0] != T.shape[1]:
raise TypeError('Transition matrix on index' + ' ' +
str(idx) + 'must be ' +
'a square matrix.')
if T.shape[0] != g.nv():
raise TypeError('Propagation matrix must ' +
'have the same dimension ' +
'as the number of vertices.')
else:
T = g.get_adjacency_matrix()
i += 1
transition_matrix[i] = (T.T / np.sum(T, axis=1)).T
label = g.get_labels(purpose='adjacency')
try:
labels |= set(itervalues(label))
except TypeError:
raise TypeError(
'For a non attributed kernel, labels should be hashable.'
)
L.append((g.nv(), label))
if i == -1:
raise ValueError('Parsed input is empty')
# The number of parsed graphs
n = i + 1
# enumerate labels
if self._method_calling == 1:
enum_labels = {l: i for (i, l) in enumerate(list(labels))}
self._enum_labels = enum_labels
self._parent_labels = labels
elif self._method_calling == 3:
new_elements = labels - self._parent_labels
if len(new_elements) > 0:
new_enum_labels = iter((l, i) for (i, l) in enumerate(
list(new_elements), len(self._enum_labels)))
enum_labels = dict(
chain(iteritems(self._enum_labels), new_enum_labels))
else:
enum_labels = self._enum_labels
# make a matrix for all graphs that contains label vectors
P, data, indexes = dict(), list(), [0]
for (k, (nv, label)) in enumerate(L):
data += [(indexes[-1] + j, enum_labels[label[j]])
for j in range(nv)]
indexes.append(indexes[-1] + nv)
# Initialise the on hot vector
rows, cols = zip(*data)
P = np.zeros(shape=(indexes[-1], len(enum_labels)))
P[rows, cols] = 1
dim_orig = len(self._enum_labels)
# feature vectors
if self._method_calling == 1:
# simple normal
self._u, self._b, self._hd = list(), list(), list()
for t in range(self.t_max):
u = self.random_state_.randn(len(enum_labels))
if self.take_cauchy_:
# cauchy
u = np.divide(
u, self.random_state_.randn(len(enum_labels)))
self._u.append(u)
# random offset
self._b.append(self.w * self.random_state_.rand())
phi = {k: dict() for k in range(n)}
for t in range(self.t_max):
# for hash all graphs inside P and produce the feature vectors
hashes = self.calculate_LSH(P, self._u[t], self._b[t])
hd = dict(
(j, i) for i, j in enumerate(set(np.unique(hashes))))
self._hd.append(hd)
features = np.vectorize(lambda i: hd[i])(hashes)
# Accumulate the results.
for k in range(n):
phi[k][t] = Counter(features[indexes[k]:indexes[k +
1]])
# calculate the Propagation matrix if needed
if t < self.t_max - 1:
for k in range(n):
start, end = indexes[k:k + 2]
P[start:end, :] = np.dot(transition_matrix[k],
P[start:end, :])
return [phi[k] for k in range(n)]
elif (self._method_calling == 3 and dim_orig >= len(enum_labels)):
phi = {k: dict() for k in range(n)}
for t in range(self.t_max):
# for hash all graphs inside P and produce the feature vectors
hashes = self.calculate_LSH(P, self._u[t], self._b[t])
hd = dict(
chain(
iteritems(self._hd[t]),
iter((j, i)
for i, j in enumerate(
filterfalse(lambda x: x in self._hd[t],
np.unique(hashes)),
len(self._hd[t])))))
features = np.vectorize(lambda i: hd[i])(hashes)
# Accumulate the results.
for k in range(n):
phi[k][t] = Counter(features[indexes[k]:indexes[k +
1]])
# calculate the Propagation matrix if needed
if t < self.t_max - 1:
for k in range(n):
start, end = indexes[k:k + 2]
P[start:end, :] = np.dot(transition_matrix[k],
P[start:end, :])
return [phi[k] for k in range(n)]
else:
cols = np.array(cols)
vertices = np.where(cols < dim_orig)[0]
vertices_p = np.where(cols >= dim_orig)[0]
nnv = len(enum_labels) - dim_orig
phi = {k: dict() for k in range(n)}
for t in range(self.t_max):
# hash all graphs inside P and produce the feature vectors
hashes = self.calculate_LSH(P[vertices, :dim_orig],
self._u[t], self._b[t])
hd = dict(
chain(
iteritems(self._hd[t]),
iter((j, i)
for i, j in enumerate(
filterfalse(lambda x: x in self._hd[t],
np.unique(hashes)),
len(self._hd[t])))))
features = np.vectorize(lambda i: hd[i],
otypes=[int])(hashes)
# for each the new labels graph hash P and produce the feature vectors
u = self.random_state_.randn(nnv)
if self.take_cauchy_:
# cauchy
u = np.divide(u, self.random_state_.randn(nnv))
u = np.hstack((self._u[t], u))
# calculate hashes for the remaining
hashes = self.calculate_LSH(P[vertices_p, :], u,
self._b[t])
hd = dict(
chain(
iteritems(hd),
iter((j, i)
for i, j in enumerate(hashes, len(hd)))))
features_p = np.vectorize(lambda i: hd[i],
otypes=[int])(hashes)
# Accumulate the results
for k in range(n):
A = Counter(features[np.logical_and(
indexes[k] <= vertices,
vertices <= indexes[k + 1])])
B = Counter(features_p[np.logical_and(
indexes[k] <= vertices_p,
vertices_p <= indexes[k + 1])])
phi[k][t] = A + B
# calculate the Propagation matrix if needed
if t < self.t_max - 1:
for k in range(n):
start, end = indexes[k:k + 2]
P[start:end, :] = np.dot(transition_matrix[k],
P[start:end, :])
Q = np.all(P[:, dim_orig:] > 0, axis=1)
vertices = np.where(~Q)[0]
vertices_p = np.where(Q)[0]
return [phi[k] for k in range(n)]
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 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 parse_input(self, X):
"""Parse and create features for the NSPD 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
-------
M : dict
A dictionary with keys all the distances from 0 to self.d
and values the the np.arrays with rows corresponding to the
non-null input graphs and columns to the enumerations of tuples
consisting of pairs of hash values and radius, from all the given
graphs of the input (plus the fitted one's on transform).
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
# Hold the number of graphs
ng = 0
# Holds all the data for combinations of r, d
data = collections.defaultdict(dict)
# Index all keys for combinations of r, d
all_keys = collections.defaultdict(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, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element' +
' on index: ' + str(idx))
continue
else:
g = Graph(x[0], x[1], x[2])
g.change_format("adjacency")
elif type(x) is Graph:
g = Graph(
x.get_adjacency_matrix(),
x.get_labels(purpose="adjacency", label_type="vertex"),
x.get_labels(purpose="adjacency", label_type="edge"))
else:
raise TypeError('each element of X must have either ' +
'a graph with labels for node and edge ' +
'or 3 elements consisting of a graph ' +
'type object, labels for vertices and ' +
'labels for edges.')
# Bring to the desired format
g.change_format(self._graph_format)
# Take the vertices
vertices = set(g.get_vertices(purpose=self._graph_format))
# Extract the dicitionary
ed = g.get_edge_dictionary()
# Convert edges to tuples
edges = {(j, k) for j in ed.keys() for k in ed[j].keys()}
# Extract labels for nodes
Lv = g.get_labels(purpose=self._graph_format)
# and for edges
Le = g.get_labels(purpose=self._graph_format,
label_type="edge")
# Produce all the neighborhoods and the distance pairs
# up to the desired radius and maximum distance
N, D, D_pair = g.produce_neighborhoods(self.r,
purpose="dictionary",
with_distances=True,
d=self.d)
# Hash all the neighborhoods
H = self._hash_neighborhoods(vertices, edges, Lv, Le, N,
D_pair)
if self._method_calling == 1:
for d in filterfalse(lambda x: x not in D,
range(self.d + 1)):
for (A, B) in D[d]:
for r in range(self.r + 1):
key = (H[r, A], H[r, B])
keys = all_keys[r, d]
idx = keys.get(key, None)
if idx is None:
idx = len(keys)
keys[key] = idx
data[r, d][ng, idx] = data[r, d].get(
(ng, idx), 0) + 1
elif self._method_calling == 3:
for d in filterfalse(lambda x: x not in D,
range(self.d + 1)):
for (A, B) in D[d]:
# Based on the edges of the bidirected graph
for r in range(self.r + 1):
keys = all_keys[r, d]
fit_keys = self._fit_keys[r, d]
key = (H[r, A], H[r, B])
idx = fit_keys.get(key, None)
if idx is None:
idx = keys.get(key, None)
if idx is None:
idx = len(keys) + len(fit_keys)
keys[key] = idx
data[r, d][ng, idx] = data[r, d].get(
(ng, idx), 0) + 1
ng += 1
if ng == 0:
raise ValueError('parsed input is empty')
if self._method_calling == 1:
# A feature matrix for all levels
M = dict()
for (key, d) in filterfalse(lambda a: len(a[1]) == 0,
iteritems(data)):
indexes, data = zip(*iteritems(d))
rows, cols = zip(*indexes)
M[key] = csr_matrix((data, (rows, cols)),
shape=(ng, len(all_keys[key])),
dtype=np.int64)
self._fit_keys = all_keys
self._ngx = ng
elif self._method_calling == 3:
# A feature matrix for all levels
M = dict()
for (key, d) in filterfalse(lambda a: len(a[1]) == 0,
iteritems(data)):
indexes, data = zip(*iteritems(d))
rows, cols = zip(*indexes)
M[key] = csr_matrix(
(data, (rows, cols)),
shape=(ng,
len(all_keys[key]) + len(self._fit_keys[key])),
dtype=np.int64)
self._ngy = ng
return M
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 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`.
"""
if self.base_graph_kernel_ is None:
raise ValueError('User must provide a base_graph_kernel')
# Input validation and parsing
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
nx, labels = 0, list()
if self._method_calling in [1, 2]:
nl, labels_enum, base_graph_kernel = 0, dict(), dict()
for kidx in range(self.n_iter):
base_graph_kernel[kidx] = self.base_graph_kernel_[0](
**self.base_graph_kernel_[1])
elif self._method_calling == 3:
nl, labels_enum, base_graph_kernel = len(
self._labels_enum), dict(self._labels_enum), self.X
inp = list()
neighbors = list()
for (idx, x) in enumerate(iter(X)):
is_iter = False
if isinstance(x, collections.Iterable):
x, is_iter = list(x), True
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='any',
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:
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')
label = x.get_labels(purpose='any')
inp.append((x.get_graph_object(), extra))
neighbors.append(x.get_edge_dictionary())
labels.append(label)
for v in set(itervalues(label)):
if v not in labels_enum:
labels_enum[v] = nl
nl += 1
nx += 1
if nx == 0:
raise ValueError('parsed input is empty')
# Calculate the hadamard matrix
H = hadamard(int(2**(ceil(log2(nl)))))
def generate_graphs(labels):
# Intial labeling of vertices based on their corresponding Hadamard code (i-th row of the
# Hadamard matrix) where i is the i-th label on enumeration
new_graphs, new_labels = list(), list()
for ((obj, extra), label) in zip(inp, labels):
new_label = dict()
for (k, v) in iteritems(label):
new_label[k] = H[labels_enum[v], :]
new_graphs.append(
(obj, {i: tuple(j)
for (i, j) in iteritems(new_label)}) + extra)
new_labels.append(new_label)
yield new_graphs
# Main
for i in range(1, self.n_iter):
new_graphs, labels, new_labels = list(), new_labels, list()
for ((obj, extra), neighbor,
old_label) in zip(inp, neighbors, labels):
# Find unique labels and sort them for both graphs and keep for each node
# the temporary
new_label = dict()
for (k, ns) in iteritems(neighbor):
new_label[k] = old_label[k]
for q in ns:
new_label[k] = np.add(new_label[k], old_label[q])
new_labels.append(new_label)
new_graphs.append(
(obj, {i: tuple(j)
for (i, j) in iteritems(new_label)}) + extra)
yield new_graphs
if self._method_calling in [1, 2]:
base_graph_kernel = {
i: self.base_graph_kernel_[0](**self.base_graph_kernel_[1])
for i in range(self.n_iter)
}
if self._parallel is None:
# Add the zero iteration element
if self._method_calling == 1:
for (i, g) in enumerate(generate_graphs(labels)):
base_graph_kernel[i].fit(g)
elif self._method_calling == 2:
K = np.sum((base_graph_kernel[i].fit_transform(g)
for (i, g) in enumerate(generate_graphs(labels))),
axis=0)
elif self._method_calling == 3:
# Calculate the kernel matrix without parallelization
K = np.sum((self.X[i].transform(g)
for (i, g) in enumerate(generate_graphs(labels))),
axis=0)
else:
if self._method_calling == 1:
self._parallel(
joblib.delayed(efit)(base_graph_kernel[i], g)
for (i, g) in enumerate(generate_graphs(labels)))
elif self._method_calling == 2:
# Calculate the kernel marix with parallelization
K = np.sum(self._parallel(
joblib.delayed(efit_transform)(base_graph_kernel[i], g)
for (i, g) in enumerate(generate_graphs(labels))),
axis=0)
elif self._method_calling == 3:
# 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(labels))),
axis=0)
if self._method_calling == 1:
self._labels_enum = labels_enum
return base_graph_kernel
elif self._method_calling == 2:
self._labels_enum = labels_enum
return K, base_graph_kernel
elif self._method_calling == 3:
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 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 and create features for the `subgraph_matching` 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
out = list()
for (idx, x) in enumerate(iter(X)):
is_iter = False
if isinstance(x, collections.Iterable):
is_iter = True
x = list(x)
if type(x) is Graph:
g = Graph(
x.get_adjacency_matrix(),
x.get_labels(purpose="adjacency"),
x.get_labels(purpose="adjacency", label_type="edge"),
self._graph_format)
elif is_iter and len(x) in [0, 3]:
x = list(x)
if len(x) == 0:
warnings.warn('Ignoring empty element' +
' on index: ' + str(idx))
continue
elif len(x) == 3:
g = Graph(x[0], x[1], x[2], "adjacency")
g.change_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, ' +
'edge labels dict \n')
n = g.nv()
E = g.get_edge_dictionary()
L = g.get_labels(purpose="dictionary",
return_none=(self.kv is None))
Le = g.get_labels(purpose="dictionary",
label_type="edge",
return_none=(self.ke is None))
Er = set(
(a, b) for a in E.keys() for b in E[a].keys() if a != b)
i += 1
out.append((n, Er, L, Le))
if i == 0:
raise ValueError('parsed input is empty')
return out
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