#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Oct 07 2019
@author: Nathan de Lara <nathan.delara@polytechnique.org>
"""
from typing import Union
import numpy as np
from scipy import sparse
from sknetwork.linalg import SVDSolver, LanczosSVD
from sknetwork.ranking.base import BaseRanking
from sknetwork.utils.check import check_format
[docs]class HITS(BaseRanking):
"""Hub and authority scores of each node.
For bipartite graphs, the hub score is computed on rows and the authority score on columns.
Parameters
----------
solver : ``'lanczos'`` (default, Lanczos algorithm) or :class:`SVDSolver` (custom solver)
Which solver to use.
Attributes
----------
scores_ : np.ndarray
Hub score of each node.
scores_row_ : np.ndarray
Hub score of each row, for bipartite graphs.
scores_col_ : np.ndarray
Authority score of each column, for bipartite graphs.
Example
-------
>>> from sknetwork.ranking import HITS
>>> from sknetwork.data import star_wars
>>> hits = HITS()
>>> biadjacency = star_wars()
>>> scores = hits.fit_predict(biadjacency)
>>> np.round(scores, 2)
array([0.5 , 0.23, 0.69, 0.46])
References
----------
Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment.
Journal of the ACM, 46(5), 604-632.
"""
def __init__(self, solver: Union[str, SVDSolver] = 'lanczos'):
super(HITS, self).__init__()
if type(solver) == str:
self.solver: SVDSolver = LanczosSVD()
else:
self.solver = solver
[docs] def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray]) -> 'HITS':
"""Compute HITS algorithm with a spectral method.
Parameters
----------
adjacency :
Adjacency or biadjacency matrix of the graph.
Returns
-------
self: :class:`HITS`
"""
adjacency = check_format(adjacency)
self.solver.fit(adjacency, 1)
hubs: np.ndarray = self.solver.singular_vectors_left_.reshape(-1)
authorities: np.ndarray = self.solver.singular_vectors_right_.reshape(-1)
h_pos, h_neg = (hubs > 0).sum(), (hubs < 0).sum()
a_pos, a_neg = (authorities > 0).sum(), (authorities < 0).sum()
if h_pos > h_neg:
hubs = np.clip(hubs, a_min=0., a_max=None)
else:
hubs = np.clip(-hubs, a_min=0., a_max=None)
if a_pos > a_neg:
authorities = np.clip(authorities, a_min=0., a_max=None)
else:
authorities = np.clip(-authorities, a_min=0., a_max=None)
self.scores_row_ = hubs
self.scores_col_ = authorities
self.scores_ = hubs
return self