LexRank.py

import numpy as np
from scipy.sparse.csgraph import connected_components
from scipy.special import softmax
import logging

logger = logging.getLogger(__name__)

def degree_centrality_scores(
    similarity_matrix,
    threshold=None,
    increase_power=True,
):
    if not (
        threshold is None
        or isinstance(threshold, float)
        and 0 <= threshold < 1
    ):
        raise ValueError(
            '\'threshold\' should be a floating-point number '
            'from the interval [0, 1) or None',
        )

    if threshold is None:
        markov_matrix = create_markov_matrix(similarity_matrix)

    else:
        markov_matrix = create_markov_matrix_discrete(
            similarity_matrix,
            threshold,
        )

    scores = stationary_distribution(
        markov_matrix,
        increase_power=increase_power,
        normalized=False,
    )

    return scores


def _power_method(transition_matrix, increase_power=True, max_iter=10000):
    eigenvector = np.ones(len(transition_matrix))

    if len(eigenvector) == 1:
        return eigenvector

    transition = transition_matrix.transpose()

    for _ in range(max_iter):
        eigenvector_next = np.dot(transition, eigenvector)

        if np.allclose(eigenvector_next, eigenvector):
            return eigenvector_next

        eigenvector = eigenvector_next

        if increase_power:
            transition = np.dot(transition, transition)

    logger.warning("Maximum number of iterations for power method exceeded without convergence!")
    return eigenvector_next


def connected_nodes(matrix):
    _, labels = connected_components(matrix)

    groups = []

    for tag in np.unique(labels):
        group = np.where(labels == tag)[0]
        groups.append(group)

    return groups


def create_markov_matrix(weights_matrix):
    n_1, n_2 = weights_matrix.shape
    if n_1 != n_2:
        raise ValueError('\'weights_matrix\' should be square')

    row_sum = weights_matrix.sum(axis=1, keepdims=True)

    # normalize probability distribution differently if we have negative transition values
    if np.min(weights_matrix) <= 0:
        return softmax(weights_matrix, axis=1)

    return weights_matrix / row_sum


def create_markov_matrix_discrete(weights_matrix, threshold):
    discrete_weights_matrix = np.zeros(weights_matrix.shape)
    ixs = np.where(weights_matrix >= threshold)
    discrete_weights_matrix[ixs] = 1

    return create_markov_matrix(discrete_weights_matrix)


def stationary_distribution(
    transition_matrix,
    increase_power=True,
    normalized=True,
):
    n_1, n_2 = transition_matrix.shape
    if n_1 != n_2:
        raise ValueError('\'transition_matrix\' should be square')

    distribution = np.zeros(n_1)

    grouped_indices = connected_nodes(transition_matrix)

    for group in grouped_indices:
        t_matrix = transition_matrix[np.ix_(group, group)]
        eigenvector = _power_method(t_matrix, increase_power=increase_power)
        distribution[group] = eigenvector

    if normalized:
        distribution /= n_1

    return distribution