#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on May 2020
@author: Nathan de Lara <nathan.delara@polytechnique.org>
"""
from typing import Union
import numpy as np
from scipy import sparse
from scipy.sparse.linalg import LinearOperator
from sknetwork.linalg.polynome import Polynome
from sknetwork.ranking.base import BaseRanking
from sknetwork.utils.check import check_format
from sknetwork.utils.format import get_adjacency
[docs]class Katz(BaseRanking):
"""Katz centrality, defined by:
:math:`\\sum_{k=1}^K\\alpha^k(A^k)^T\\mathbf{1}`
where :math:`A` is the adjacency matrix, :math:`\\alpha` is the damping factor and :math:`K` is the path length.
Parameters
----------
damping_factor : float
Damping factor for path contributions.
path_length : int
Maximum length of the paths.
Attributes
----------
scores_ : np.ndarray
Score of each node.
scores_row_: np.ndarray
Scores of rows, for bipartite graphs.
scores_col_: np.ndarray
Scores of columns, for bipartite graphs.
Examples
--------
>>> from sknetwork.data.toy_graphs import house
>>> adjacency = house()
>>> katz = Katz()
>>> scores = katz.fit_predict(adjacency)
>>> np.round(scores, 2)
array([6.5 , 8.25, 5.62, 5.62, 8.25])
References
----------
Katz, L. (1953). `A new status index derived from sociometric analysis
<https://link.springer.com/content/pdf/10.1007/BF02289026.pdf>`_. Psychometrika, 18(1), 39-43.
"""
def __init__(self, damping_factor: float = 0.5, path_length: int = 4):
super(Katz, self).__init__()
self.damping_factor = damping_factor
self.path_length = path_length
self.bipartite = None
[docs] def fit(self, input_matrix: Union[sparse.csr_matrix, np.ndarray, LinearOperator]) -> 'Katz':
"""Katz centrality.
Parameters
----------
input_matrix :
Adjacency matrix or biadjacency matrix of the graph.
Returns
-------
self: :class:`Katz`
"""
input_matrix = check_format(input_matrix)
adjacency, self.bipartite = get_adjacency(input_matrix)
n = adjacency.shape[0]
coefs = self.damping_factor ** np.arange(self.path_length + 1)
coefs[0] = 0.
polynome = Polynome(adjacency.T.astype(bool).tocsr(), coefs)
self.scores_ = polynome.dot(np.ones(n))
if self.bipartite:
self._split_vars(input_matrix.shape)
return self