#

Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

#

Source code for networkx.algorithms.node_classification.hmn

"""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