def __call__(self, X, ij, lmin=0, timing=False):
"""Compute a list of pairwise similarities between graphs.
Parameters
----------
X: list of N graphs
The graphs must all have same node and edge attributes.
ij: list of pairs of ints
Pair indices for which the graph kernel is to be evaluated.
lmin: 0 or 1
Number of steps to skip in each random walk path before similarity
is computed.
(lmin + 1) corresponds to the starting value of l in the summation
of Eq. 1 in Tang & de Jong, 2019 https://doi.org/10.1063/1.5078640
(or the first unnumbered equation in Section 3.3 of Kashima, Tsuda,
and Inokuchi, 2003).
Returns
-------
gramian: ndarray
A vector with the same length as ij
"""
timer = Timer()
backend = self.backend
traits = self.traits(lmin=lmin, )
''' assert graph attributes are compatible with each other '''
pred_or_tuple = Graph.has_unified_types(X)
if pred_or_tuple is not True:
group, first, second = pred_or_tuple
raise TypeError(
f'The two graphs have mismatching {group} attributes or '
'attribute types. If the attributes match in name but differ '
'in type, try `Graph.unify_datatype` as an automatic fix.\n'
f'First graph: {first}\n'
f'Second graph: {second}\n')
''' generate jobs '''
timer.tic('generating jobs')
jobs = backend.array(
np.array(ij, dtype=np.uint32).ravel().view(
dtype=np.dtype([('i', np.uint32), ('j', np.uint32)])))
timer.toc('generating jobs')
''' create output buffer '''
timer.tic('creating output buffer')
gramian = backend.empty(len(jobs), np.float32)
timer.toc('creating output buffer')
''' call GPU kernel '''
timer.tic('calling GPU kernel (overall)')
backend(
X,
self.node_kernel,
self.edge_kernel,
self.p,
self.q,
self.eps,
self.ftol,
self.gtol,
jobs,
gramian,
traits,
timer,
)
timer.toc('calling GPU kernel (overall)')
''' collect result '''
timer.tic('collecting result')
gramian = gramian.astype(self.element_dtype)
timer.toc('collecting result')
if timing:
timer.report(unit='ms')
timer.reset()
return gramian
def __call__(self,
X,
Y=None,
eval_gradient=False,
nodal=False,
lmin=0,
timing=False):
"""Compute pairwise similarity matrix between graphs
Parameters
----------
X: list of N graphs
The graphs must all have same node and edge attributes.
Y: None or list of M graphs
The graphs must all have same node and edge attributes.
eval_gradient: Boolean
If True, computes the gradient of the kernel matrix with respect
to hyperparameters and return it alongside the kernel matrix.
nodal: bool
If True, return node-wise similarities; otherwise, return graphwise
similarities.
lmin: 0 or 1
Number of steps to skip in each random walk path before similarity
is computed.
(lmin + 1) corresponds to the starting value of l in the summation
of Eq. 1 in Tang & de Jong, 2019 https://doi.org/10.1063/1.5078640
(or the first unnumbered equation in Section 3.3 of Kashima, Tsuda,
and Inokuchi, 2003).
Returns
-------
kernel_matrix: ndarray
if Y is None, return a square matrix containing pairwise
similarities between the graphs in X; otherwise, returns a matrix
containing similarities across graphs in X and Y.
gradient: ndarray
The gradient of the kernel matrix with respect to kernel
hyperparameters. Only returned if eval_gradient is True.
"""
timer = Timer()
backend = self.backend
traits = self.traits(symmetric=Y is None,
nodal=nodal,
lmin=lmin,
eval_gradient=eval_gradient)
''' assert graph attributes are compatible with each other '''
all_graphs = list(it.chain(X, Y)) if Y is not None else X
pred_or_tuple = Graph.has_unified_types(all_graphs)
if pred_or_tuple is not True:
group, first, second = pred_or_tuple
raise TypeError(
f'The two graphs have mismatching {group} attributes or '
'attribute types. If the attributes match in name but differ '
'in type, try `Graph.unify_datatype` as an automatic fix.\n'
f'First graph: {first}\n'
f'Second graph: {second}\n')
''' generate jobs '''
timer.tic('generating jobs')
if traits.symmetric:
i, j = np.triu_indices(len(X))
i, j = i.astype(np.uint32), j.astype(np.uint32)
else:
i, j = np.indices((len(X), len(Y)), dtype=np.uint32)
j += len(X)
jobs = backend.array(
np.column_stack((i.ravel(), j.ravel())).ravel().view(
np.dtype([('i', np.uint32), ('j', np.uint32)])))
timer.toc('generating jobs')
''' create output buffer '''
timer.tic('creating output buffer')
if traits.symmetric:
starts = backend.zeros(len(X) + 1, dtype=np.uint32)
if traits.nodal is True:
sizes = np.array([len(g.nodes) for g in X], dtype=np.uint32)
np.cumsum(sizes, out=starts[1:])
n_nodes_X = int(starts[-1])
output_shape = (n_nodes_X, n_nodes_X)
else:
starts[:] = np.arange(len(X) + 1)
output_shape = (len(X), len(X))
else:
starts = backend.zeros(len(X) + len(Y) + 1, dtype=np.uint32)
if traits.nodal is True:
sizes = np.array([len(g.nodes)
for g in X] + [len(g.nodes) for g in Y],
dtype=np.uint32)
np.cumsum(sizes, out=starts[1:])
n_nodes_X = int(starts[len(X)])
starts[len(X):] -= n_nodes_X
n_nodes_Y = int(starts[-1])
output_shape = (n_nodes_X, n_nodes_Y)
else:
starts[:len(X)] = np.arange(len(X))
starts[len(X):] = np.arange(len(Y) + 1)
output_shape = (len(X), len(Y))
gramian = backend.empty(int(np.prod(output_shape)), np.float32)
if traits.eval_gradient is True:
gradient = backend.empty(self.n_dims * int(np.prod(output_shape)),
np.float32)
else:
gradient = None
timer.toc('creating output buffer')
''' call GPU kernel '''
timer.tic('calling GPU kernel (overall)')
backend(
np.concatenate((X, Y)) if Y is not None else X,
self.node_kernel,
self.edge_kernel,
self.p,
self.q,
self.eps,
self.ftol,
self.gtol,
jobs,
starts,
gramian,
gradient,
output_shape[0],
output_shape[1],
self.n_dims,
traits,
timer,
)
timer.toc('calling GPU kernel (overall)')
''' collect result '''
timer.tic('collecting result')
gramian = gramian.reshape(*output_shape, order='F')
if gradient is not None:
gradient = gradient.reshape((*output_shape, self.n_dims),
order='F')[:, :,
self.active_theta_mask]
timer.toc('collecting result')
if timing:
timer.report(unit='ms')
timer.reset()
if traits.eval_gradient is True:
return (gramian.astype(self.element_dtype),
gradient.astype(self.element_dtype))
else:
return gramian.astype(self.element_dtype)
def diag(self,
X,
eval_gradient=False,
nodal=False,
lmin=0,
active_theta_only=True,
timing=False):
"""Compute the self-similarities for a list of graphs
Parameters
----------
X: list of N graphs
The graphs must all have same node attributes and edge attributes.
eval_gradient: Boolean
If True, computes the gradient of the kernel matrix with respect
to hyperparameters and return it alongside the kernel matrix.
nodal: bool
If True, returns a vector containing nodal self similarties; if
False, returns a vector containing graphs' overall self
similarities; if 'block', return a list of square matrices which
forms a block-diagonal matrix, where each diagonal block represents
the pairwise nodal similarities within a graph.
lmin: 0 or 1
Number of steps to skip in each random walk path before similarity
is computed.
(lmin + 1) corresponds to the starting value of l in the summation
of Eq. 1 in Tang & de Jong, 2019 https://doi.org/10.1063/1.5078640
(or the first unnumbered equation in Section 3.3 of Kashima, Tsuda,
and Inokuchi, 2003).
active_theta_only: bool
Whether or not to return only gradients with regard to the
non-fixed hyperparameters.
Returns
-------
diagonal: numpy.array or list of np.array(s)
If nodal=True, returns a vector containing nodal self similarties;
if nodal=False, returns a vector containing graphs' overall self
similarities; if nodal = 'block', return a list of square matrices,
each being a pairwise nodal similarity matrix within a graph.
gradient
The gradient of the kernel matrix with respect to kernel
hyperparameters. Only returned if eval_gradient is True.
"""
timer = Timer()
backend = self.backend
traits = self.traits(diagonal=True,
nodal=nodal,
lmin=lmin,
eval_gradient=eval_gradient)
''' assert graph attributes are compatible with each other '''
pred_or_tuple = Graph.has_unified_types(X)
if pred_or_tuple is not True:
group, first, second = pred_or_tuple
raise TypeError(
f'The two graphs have mismatching {group} attributes or '
'attribute types.'
'If the attribute names do match, then try to unify data '
'types automatically with `Graph.unify_datatype`.\n'
f'First graph: {first}\n'
f'Second graph: {second}\n')
''' generate jobs '''
timer.tic('generating jobs')
i = np.arange(len(X), dtype=np.uint32)
jobs = backend.array(
np.column_stack((i, i)).ravel().view(
np.dtype([('i', np.uint32), ('j', np.uint32)])))
timer.toc('generating jobs')
''' create output buffer '''
timer.tic('creating output buffer')
starts = backend.zeros(len(X) + 1, dtype=np.uint32)
if nodal is True:
sizes = np.array([len(g.nodes) for g in X], dtype=np.uint32)
np.cumsum(sizes, out=starts[1:])
output_length = int(starts[-1])
elif nodal is False:
starts[:] = np.arange(len(X) + 1)
output_length = len(X)
elif nodal == 'block':
sizes = np.array([len(g.nodes) for g in X], dtype=np.uint32)
np.cumsum(sizes**2, out=starts[1:])
output_length = int(starts[-1])
else:
raise ValueError("Invalid 'nodal' option '%s'" % nodal)
gramian = backend.empty(output_length, np.float32)
if traits.eval_gradient is True:
gradient = backend.empty(self.n_dims * output_length, np.float32)
else:
gradient = None
timer.toc('creating output buffer')
''' call GPU kernel '''
timer.tic('calling GPU kernel (overall)')
backend(
X,
self.node_kernel,
self.edge_kernel,
self.p,
self.q,
self.eps,
self.ftol,
self.gtol,
jobs,
starts,
gramian,
gradient,
output_length,
1,
self.n_dims,
traits,
timer,
)
timer.toc('calling GPU kernel (overall)')
''' post processing '''
timer.tic('collecting result')
if gradient is not None:
gradient = gradient.reshape((output_length, self.n_dims),
order='F')
if active_theta_only:
gradient = gradient[:, self.active_theta_mask]
if nodal == 'block':
retval = [
gramian[s:s + n**2].reshape(n, n)
for s, n in zip(starts[:-1], sizes)
]
elif traits.eval_gradient is True:
retval = (gramian.astype(self.element_dtype),
gradient.astype(self.element_dtype))
else:
retval = gramian.astype(self.element_dtype)
timer.toc('collecting result')
if timing:
timer.report(unit='ms')
timer.reset()
return retval
def __call__(self,
X,
Y=None,
eval_gradient=False,
lmin=0,
return_hotspot=False,
timing=False):
'''Computes the distance matrix and optionally its gradient with respect
to hyperparameters.
Parameters
----------
X: list of graphs
The first dataset to be compared.
Y: list of graphs or None
The second dataset to be compared. If None, X will be compared with
itself.
eval_gradient: bool
If True, returns the gradient of the weight matrix alongside the
matrix itself.
lmin: 0 or 1
Number of steps to skip in each random walk path before similarity
is computed.
(lmin + 1) corresponds to the starting value of l in the summation
of Eq. 1 in Tang & de Jong, 2019 https://doi.org/10.1063/1.5078640
(or the first unnumbered equation in Section 3.3 of Kashima, Tsuda,
and Inokuchi, 2003).
return_hotspot: bool
Whether or not to return the indices of the node pairs that
determines the maximin distance between the graphs. Generally,
these hotspots represent the location of the largest difference
between the graphs.
options: keyword arguments
Additional arguments to be passed to the underlying kernel.
Returns
-------
distance: 2D matrix
A distance matrix between the data points.
hotspot: a pair of 2D integer matrices
Indices of the hotspot node pairs between the graphs. Only
returned if the ``return_hotspot`` argument is True.
gradient: 3D tensor
A tensor where the i-th frontal slide [:, :, i] contain the partial
derivative of the distance matrix with respect to the i-th
hyperparameter. Only returned if the ``eval_gradient`` argument
is True.
'''
timer = Timer()
backend = self.maximin_backend
traits = self.traits(symmetric=Y is None,
nodal=False,
lmin=lmin,
eval_gradient=eval_gradient)
''' assert graph attributes are compatible with each other '''
all_graphs = list(it.chain(X, Y)) if Y is not None else X
pred_or_tuple = Graph.has_unified_types(all_graphs)
if pred_or_tuple is not True:
group, first, second = pred_or_tuple
raise TypeError(
f'The two graphs have mismatching {group} attributes or '
'attribute types. If the attributes match in name but differ '
'in type, try `Graph.unify_datatype` as an automatic fix.\n'
f'First graph: {first}\n'
f'Second graph: {second}\n')
''' generate jobs '''
timer.tic('generating jobs')
if traits.symmetric:
i, j = np.triu_indices(len(X))
i, j = i.astype(np.uint32), j.astype(np.uint32)
else:
i, j = np.indices((len(X), len(Y)), dtype=np.uint32)
j += len(X)
jobs = backend.array(
np.column_stack((i.ravel(), j.ravel())).ravel().view(
np.dtype([('i', np.uint32), ('j', np.uint32)])))
timer.toc('generating jobs')
''' create output buffer '''
timer.tic('creating output buffer')
if traits.symmetric:
output_shape = (len(X), len(X))
starts = backend.zeros(len(X) + 1, dtype=np.uint32)
starts[:] = np.arange(len(X) + 1)
starts_nodal = backend.zeros(len(X) + 1, dtype=np.uint32)
sizes = np.array([len(g.nodes) for g in X], dtype=np.uint32)
np.cumsum(sizes, out=starts_nodal[1:])
diag = super().diag(X,
eval_gradient,
nodal=True,
lmin=lmin,
active_theta_only=False)
else:
output_shape = (len(X), len(Y))
XY = np.concatenate((X, Y))
starts = backend.zeros(len(X) + len(Y) + 1, dtype=np.uint32)
starts[:len(X)] = np.arange(len(X))
starts[len(X):] = np.arange(len(Y) + 1)
starts_nodal = backend.zeros(len(XY) + 1, dtype=np.uint32)
sizes = np.array([len(g.nodes) for g in XY], dtype=np.uint32)
np.cumsum(sizes, out=starts_nodal[1:])
diag = super().diag(XY,
eval_gradient,
nodal=True,
lmin=lmin,
active_theta_only=False)
distance = backend.empty(int(np.prod(output_shape)), np.float32)
hotspot = backend.empty(int(np.prod(output_shape)), np.int32)
if eval_gradient is True:
gradient = backend.empty(self.n_dims * int(np.prod(output_shape)),
np.float32)
r, dr = diag
diags = [
backend.array(np.r_[r[b:e], dr[b:e, :].ravel('F')])
for b, e in zip(starts_nodal[:-1], starts_nodal[1:])
]
else:
gradient = None
diags = [
backend.array(diag[b:e])
for b, e in zip(starts_nodal[:-1], starts_nodal[1:])
]
diags_d = backend.empty(len(diags), dtype=np.uintp)
diags_d[:] = [int(d.base) for d in diags]
timer.toc('creating output buffer')
''' call GPU kernel '''
timer.tic('calling GPU kernel (overall)')
backend(
np.concatenate((X, Y)) if Y is not None else X,
diags_d,
self.node_kernel,
self.edge_kernel,
self.p,
self.q,
self.eps,
self.ftol,
self.gtol,
jobs,
starts,
distance,
hotspot,
gradient,
output_shape[0],
output_shape[1] if len(output_shape) >= 2 else 1,
self.n_dims,
traits,
timer,
)
timer.toc('calling GPU kernel (overall)')
''' collect result '''
timer.tic('collecting result')
distance = distance.reshape(*output_shape, order='F')
if gradient is not None:
gradient = gradient.reshape((*output_shape, self.n_dims),
order='F')[:, :,
self.active_theta_mask]
timer.toc('collecting result')
if timing:
timer.report(unit='ms')
timer.reset()
retval = [distance.astype(self.element_dtype)]
if return_hotspot is True:
if Y is None:
n = np.array([len(g.nodes) for g in X], dtype=np.uint32)
else:
n = np.array([len(g.nodes) for g in Y], dtype=np.uint32)
hotspot = hotspot.reshape(*output_shape, order='F')
retval.append((hotspot // n, hotspot % n))
if eval_gradient is True:
retval.append(gradient.astype(self.element_dtype))
if len(retval) == 1:
return retval[0]
else:
return tuple(retval)