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

__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 : list List of length ``len(G)`` with the predicted labels for each node. Raises ------ NetworkXError If no nodes in `G` have attribute `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). """ import numpy as np import scipy as sp import scipy.sparse # call as sp.sparse X = nx.to_scipy_sparse_array(G) # adjacency matrix labels, label_dict = _get_label_info(G, label_name) if labels.shape[0] == 0: raise nx.NetworkXError( f"No node on the input graph is labeled by '{label_name}'." ) n_samples = X.shape[0] n_classes = label_dict.shape[0] F = np.zeros((n_samples, n_classes)) # Build propagation matrix degrees = X.sum(axis=0) degrees[degrees == 0] = 1 # Avoid division by 0 # TODO: csr_array D = sp.sparse.csr_array(sp.sparse.diags((1.0 / degrees), offsets=0)) P = (D @ X).tolil() P[labels[:, 0]] = 0 # labels[:, 0] indicates IDs of labeled nodes # Build base matrix B = np.zeros((n_samples, n_classes)) B[labels[:, 0], labels[:, 1]] = 1 for _ in range(max_iter): F = (P @ F) + B return label_dict[np.argmax(F, axis=1)].tolist()