import numpy as np
import networkx as nx
import scipy.sparse as sp
from sklearn import preprocessing
from .. import BaseModel, register_model
[docs]@register_model("hope")
class HOPE(BaseModel):
r"""The HOPE model from the `"Grarep: Asymmetric transitivity preserving graph embedding"
<http://dl.acm.org/citation.cfm?doid=2939672.2939751>`_ paper.
Args:
hidden_size (int) : The dimension of node representation.
beta (float) : Parameter in katz decomposition.
"""
[docs] @staticmethod
def add_args(parser):
"""Add model-specific arguments to the parser."""
# fmt: off
parser.add_argument('--beta', type=float, default=0.01,
help='Parameter of katz for HOPE. Default is 0.01')
# fmt: on
[docs] @classmethod
def build_model_from_args(cls, args):
return cls(args.hidden_size, args.beta)
def __init__(self, dimension, beta):
super(HOPE, self).__init__()
self.dimension = dimension
self.beta = beta
[docs] def train(self, G):
r"""The author claim that Katz has superior performance in related tasks
S_katz = (M_g)^-1 * M_l = (I - beta*A)^-1 * beta*A = (I - beta*A)^-1 * (I - (I -beta*A))
= (I - beta*A)^-1 - I
"""
adj = nx.adjacency_matrix(G).todense()
n = adj.shape[0]
katz_matrix = np.asarray((np.eye(n) - self.beta * np.mat(adj)).I - np.eye(n))
self.embeddings = self._get_embedding(katz_matrix, self.dimension)
return self.embeddings
def _get_embedding(self, matrix, dimension):
# get embedding from svd and process normalization for ut and vt
ut, s, vt = sp.linalg.svds(matrix, int(dimension / 2))
emb_matrix_1, emb_matrix_2 = ut, vt.transpose()
emb_matrix_1 = emb_matrix_1 * np.sqrt(s)
emb_matrix_2 = emb_matrix_2 * np.sqrt(s)
emb_matrix_1 = preprocessing.normalize(emb_matrix_1, "l2")
emb_matrix_2 = preprocessing.normalize(emb_matrix_2, "l2")
features = np.hstack((emb_matrix_1, emb_matrix_2))
return features