"""Function for computing Harmonic function algorithm by Zhu et al.
References
----------
Zhu, X., Ghahramani, Z., & Lafferty, J. (2003, August).
Semi-supervised learning using gaussian fields and harmonic functions.
In ICML (Vol. 3, pp. 912-919).
"""
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__ = ["harmonic_function"]
[docs]@not_implemented_for("directed")
def harmonic_function(G, max_iter=30, label_name="label"):
"""Node classification by Harmonic function
Parameters
----------
G : NetworkX Graph
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.harmonic_function(G)
>>> predicted
['A', 'A', 'B', 'B']
References
----------
Zhu, X., Ghahramani, Z., & Lafferty, J. (2003, August).
Semi-supervised learning using gaussian fields and harmonic functions.
In ICML (Vol. 3, pp. 912-919).
"""
try:
import numpy as np
except ImportError as e:
raise ImportError(
"harmonic_function() requires numpy: http://numpy.org/ "
) from e
try:
from scipy import sparse
except ImportError as e:
raise ImportError(
"harmonic_function() requires scipy: http://scipy.org/ "
) from e
def _build_propagation_matrix(X, labels):
"""Build propagation matrix of Harmonic function
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
Returns
----------
P : 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
D = sparse.diags((1.0 / degrees), offsets=0)
P = D.dot(X).tolil()
P[labels[:, 0]] = 0 # labels[:, 0] indicates IDs of labeled nodes
return P
def _build_base_matrix(X, labels, n_classes):
"""Build base matrix of Harmonic function
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
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
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)
B = _build_base_matrix(X, labels, 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