def parse_input(self, X):
"""Parse and create features for svm_theta 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 lovasz metrics for the 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):
x, is_iter = list(x), True
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
else:
x = Graph(x[0], {}, {}, 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 1 ' +
'and at most 3 elements\n')
i += 1
A = x.get_adjacency_matrix()
dual_coeffs = _calculate_svm_theta_(A)
out.append(self._calculate_svm_theta_levels_(A, dual_coeffs))
if i == 0:
raise ValueError('parsed input is empty')
return out
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 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 check the given input for the Graph Hopper 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 fitting the given graph
format).
Returns
-------
out : np.array, shape=(len(X), n_labels)
A np array for frequency (cols) histograms for all Graphs (rows).
"""
if not isinstance(X, Iterable):
raise TypeError('input must be an iterable\n')
else:
ni = 0
diam = list()
graphs = list()
for (i, x) in enumerate(iter(X)):
is_iter = False
if isinstance(x, Iterable):
is_iter = True
x = list(x)
if type(x) is Graph:
g = Graph(x.get_adjacency_matrix(),
x.get_labels(purpose="adjacency"), {},
self._graph_format)
elif is_iter and len(x) == 0 or len(x) >= 2:
if len(x) == 0:
warn('Ignoring empty element on index: ' + str(i))
continue
elif len(x) >= 2:
g = Graph(x[0], x[1], {}, "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, ')
spm, attr = g.build_shortest_path_matrix(labels="vertex")
nv = g.nv()
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.'
)
diam.append(int(np.max(spm[spm < float("Inf")])))
graphs.append((g.get_adjacency_matrix(), nv, attributes))
ni += 1
if self._method_calling == 1:
max_diam = self._max_diam = max(diam) + 1
else:
max_diam = max(self._max_diam, max(diam) + 1)
out = list()
for i in range(ni):
AM, node_nr, attributes = graphs[i]
des = np.zeros(shape=(node_nr, node_nr, max_diam), dtype=int)
occ = np.zeros(shape=(node_nr, node_nr, max_diam), dtype=int)
# Convert adjacency matrix to dictionary
idx_i, idx_j = np.where(AM > 0)
ed = defaultdict(dict)
for (a, b) in filterfalse(lambda a: a[0] == a[1],
zip(idx_i, idx_j)):
ed[a][b] = AM[a, b]
for j in range(node_nr):
A = np.zeros(shape=AM.shape)
# Single-source shortest path from node j
D, p = dijkstra(ed, j)
D = np.array(
list(D.get(k, float("Inf")) for k in range(node_nr)))
p[j] = -1
# Restrict to the connected component of node j
conn_comp = np.where(D < float("Inf"))[0]
# To-be DAG adjacency matrix of connected component of node j
A_cc = A[conn_comp, :][:, conn_comp]
# Adjacency matrix of connected component of node j
AM_cc = AM[conn_comp, :][:, conn_comp]
D_cc = D[conn_comp]
conn_comp_converter = np.zeros(shape=(A.shape[0], 1),
dtype=int)
for k in range(conn_comp.shape[0]):
conn_comp_converter[conn_comp[k]] = k
conn_comp_converter = np.vstack([0, conn_comp_converter])
p_cc = conn_comp_converter[
np.array(list(p[k] for k in conn_comp)) + 1]
# Number of nodes in connected component of node j
conncomp_node_nr = A_cc.shape[0]
for v in range(conncomp_node_nr):
if p_cc[v] > 0:
# Generate A_cc by adding directed edges of form (parent(v), v)
A_cc[p_cc[v], v] = 1
# Distance from v to j
v_dist = D_cc[v]
# All neighbors of v in the undirected graph
v_nbs = np.where(AM_cc[v, :] > 0)[0]
# Distances of neighbors of v to j
v_nbs_dists = D_cc[v_nbs]
# All neighbors of v in undirected graph who are
# one step closer to j than v is; i.e. SP-DAG parents
v_parents = v_nbs[v_nbs_dists == (v_dist - 1)]
# Add SP-DAG parents to A_cc
A_cc[v_parents, v] = 1
# Computes the descendants & occurence vectors o_j(v), d_j(v)
# for all v in the connected component
occ_p, des_p = od_vectors_dag(A_cc, D_cc)
if des_p.shape[0] == 1 and j == 0:
des[j, 0, 0] = des_p
occ[j, 0, 0] = occ_p
else:
# Convert back to the indices of the original graph
for v in range(des_p.shape[0]):
for l in range(des_p.shape[1]):
des[j, conn_comp[v], l] = des_p[v, l]
# Convert back to the indices of the original graph
for v in range(occ_p.shape[0]):
for l in range(occ_p.shape[1]):
occ[j, conn_comp[v], l] = occ_p[v, l]
M = np.zeros(shape=(node_nr, max_diam, max_diam))
# j loops through choices of root
for j in range(node_nr):
des_mat_j_root = np.squeeze(des[j, :, :])
occ_mat_j_root = np.squeeze(occ[j, :, :])
# v loops through nodes
for v in range(node_nr):
for a in range(max_diam):
for b in range(a, max_diam):
# M[v,:,:] is M[v]; a = node coordinate in path, b = path length
M[v, a,
b] += des_mat_j_root[v, b -
a] * occ_mat_j_root[v, a]
if self.calculate_norm_:
out.append((M, attributes, np.sum(attributes**2, axis=1)))
else:
out.append((M, attributes))
return out
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 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 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):
"""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 and create features for lovasz_theta 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 lovasz metrics for the given input.
"""
if not isinstance(X, collections.Iterable):
raise TypeError('input must be an iterable\n')
else:
i = 0
adjm = list()
max_dim = 0
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) in [0, 1, 2, 3]:
if len(x) == 0:
warnings.warn('Ignoring empty element ' +
'on index: ' + str(idx))
continue
else:
x = Graph(x[0], {}, {}, 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 1 ' +
'and at most 3 elements\n')
i += 1
A = x.get_adjacency_matrix()
adjm.append(A)
max_dim = max(max_dim, A.shape[0])
if self._method_calling == 1:
if self.d_ is None:
self.d_ = max_dim + 1
if self.d_ < max_dim + 1:
if self.max_dim is None and self._method_calling == 3:
raise ValueError(
'Maximum dimension of a graph in transform is bigger '
'than the one found in fit. To avoid that use max_dim parameter.'
)
else:
raise ValueError('max_dim should correspond to the '
'biggest graph inside the dataset')
out = list()
for A in adjm:
X, t = _calculate_lovasz_embeddings_(A)
U = _calculate_lovasz_labelling_(X, t, self.d_)
out.append(self._calculate_MEC_(U))
if i == 0:
raise ValueError('parsed input is empty')
return out
