xhs-note-crawling/python/py/Lib/site-packages/networkx/algorithms/node_classification.py

"""This module provides the functions for node classification problem.

The functions in this module are not imported
into the top level `networkx` namespace.
You can access these functions by importing
the `networkx.algorithms.node_classification` modules,
then accessing the functions as attributes of `node_classification`.
For example:

  >>> from networkx.algorithms import node_classification
  >>> G = nx.path_graph(4)
  >>> G.edges()
  EdgeView([(0, 1), (1, 2), (2, 3)])
  >>> G.nodes[0]["label"] = "A"
  >>> G.nodes[3]["label"] = "B"
  >>> node_classification.harmonic_function(G)
  ['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 networkx as nx

__all__ = ["harmonic_function", "local_and_global_consistency"]


@nx.utils.not_implemented_for("directed")
@nx._dispatchable(node_attrs="label_name")
def harmonic_function(G, max_iter=30, label_name="label"):
    """Node classification by Harmonic function

    Function for computing Harmonic function algorithm by Zhu et al.

    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

    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
    D = sp.sparse.dia_array((1.0 / degrees, 0), shape=(n_samples, n_samples)).tocsr()
    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()


@nx.utils.not_implemented_for("directed")
@nx._dispatchable(node_attrs="label_name")
def local_and_global_consistency(G, alpha=0.99, max_iter=30, label_name="label"):
    """Node classification by Local and Global Consistency

    Function for computing Local and global consistency algorithm by Zhou et al.

    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 : 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.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.
    """
    import numpy as np
    import scipy as sp

    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
    D2 = sp.sparse.dia_array(
        (1.0 / np.sqrt(degrees), 0), shape=(n_samples, n_samples)
    ).tocsr()
    P = alpha * ((D2 @ X) @ D2)
    # Build base matrix
    B = np.zeros((n_samples, n_classes))
    B[labels[:, 0], labels[:, 1]] = 1 - alpha

    for _ in range(max_iter):
        F = (P @ F) + B

    return label_dict[np.argmax(F, axis=1)].tolist()


def _get_label_info(G, label_name):
    """Get and return information of labels from the input graph

    Parameters
    ----------
    G : Network X graph
    label_name : string
        Name of the target label

    Returns
    -------
    labels : numpy array, shape = [n_labeled_samples, 2]
        Array of pairs of labeled node ID and label ID
    label_dict : numpy array, shape = [n_classes]
        Array of labels
        i-th element contains the label corresponding label ID `i`
    """
    import numpy as np

    labels = []
    label_to_id = {}
    lid = 0
    for i, n in enumerate(G.nodes(data=True)):
        if label_name in n[1]:
            label = n[1][label_name]
            if label not in label_to_id:
                label_to_id[label] = lid
                lid += 1
            labels.append([i, label_to_id[label]])
    labels = np.array(labels)
    label_dict = np.array(
        [label for label, _ in sorted(label_to_id.items(), key=lambda x: x[1])]
    )
    return (labels, label_dict)