"""Function for computing Local and global consistency algorithm by Zhou et al.
References
----------
Zhou, D., Bousquet, O., Lal, T. N., Weston, J., & Schölkopf, B. (2004).
Learning with local and global consistency.
Advances in neural information processing systems, 16(16), 321-328.
"""
import networkx as nx
from networkx.utils.decorators import not_implemented_for
from networkx.algorithms.node_classification.utils import (
_get_label_info,
_init_label_matrix,
_propagate,
_predict,
)
__all__ = ["local_and_global_consistency"]
[docs]@not_implemented_for("directed")
def local_and_global_consistency(G, alpha=0.99, max_iter=30, label_name="label"):
"""Node classification by Local and Global Consistency
Parameters
----------
G : NetworkX Graph
alpha : float
Clamping factor
max_iter : int
Maximum number of iterations allowed
label_name : string
Name of target labels to predict
Returns
----------
predicted : array, shape = [n_samples]
Array of predicted labels
Raises
------
NetworkXError
If no nodes on `G` has `label_name`.
Examples
--------
>>> from networkx.algorithms import node_classification
>>> G = nx.path_graph(4)
>>> G.nodes[0]["label"] = "A"
>>> G.nodes[3]["label"] = "B"
>>> G.nodes(data=True)
NodeDataView({0: {'label': 'A'}, 1: {}, 2: {}, 3: {'label': 'B'}})
>>> G.edges()
EdgeView([(0, 1), (1, 2), (2, 3)])
>>> predicted = node_classification.local_and_global_consistency(G)
>>> predicted
['A', 'A', 'B', 'B']
References
----------
Zhou, D., Bousquet, O., Lal, T. N., Weston, J., & Schölkopf, B. (2004).
Learning with local and global consistency.
Advances in neural information processing systems, 16(16), 321-328.
"""
try:
import numpy as np
except ImportError as e:
raise ImportError(
"local_and_global_consistency() requires numpy: ", "http://numpy.org/ "
) from e
try:
from scipy import sparse
except ImportError as e:
raise ImportError(
"local_and_global_consistensy() requires scipy: ", "http://scipy.org/ "
) from e
def _build_propagation_matrix(X, labels, alpha):
"""Build propagation matrix of Local and global consistency
Parameters
----------
X : scipy sparse matrix, shape = [n_samples, n_samples]
Adjacency matrix
labels : array, shape = [n_samples, 2]
Array of pairs of node id and label id
alpha : float
Clamping factor
Returns
----------
S : scipy sparse matrix, shape = [n_samples, n_samples]
Propagation matrix
"""
degrees = X.sum(axis=0).A[0]
degrees[degrees == 0] = 1 # Avoid division by 0
D2 = np.sqrt(sparse.diags((1.0 / degrees), offsets=0))
S = alpha * D2.dot(X).dot(D2)
return S
def _build_base_matrix(X, labels, alpha, n_classes):
"""Build base matrix of Local and global consistency
Parameters
----------
X : scipy sparse matrix, shape = [n_samples, n_samples]
Adjacency matrix
labels : array, shape = [n_samples, 2]
Array of pairs of node id and label id
alpha : float
Clamping factor
n_classes : integer
The number of classes (distinct labels) on the input graph
Returns
----------
B : array, shape = [n_samples, n_classes]
Base matrix
"""
n_samples = X.shape[0]
B = np.zeros((n_samples, n_classes))
B[labels[:, 0], labels[:, 1]] = 1 - alpha
return B
X = nx.to_scipy_sparse_matrix(G) # adjacency matrix
labels, label_dict = _get_label_info(G, label_name)
if labels.shape[0] == 0:
raise nx.NetworkXError(
"No node on the input graph is labeled by '" + label_name + "'."
)
n_samples = X.shape[0]
n_classes = label_dict.shape[0]
F = _init_label_matrix(n_samples, n_classes)
P = _build_propagation_matrix(X, labels, alpha)
B = _build_base_matrix(X, labels, alpha, n_classes)
remaining_iter = max_iter
while remaining_iter > 0:
F = _propagate(P, F, B)
remaining_iter -= 1
predicted = _predict(F, label_dict)
return predicted