import time
import networkx as nx
import numpy as np
import scipy.sparse as sp
from scipy import linalg
from scipy.special import iv
from sklearn import preprocessing
from sklearn.utils.extmath import randomized_svd
from .. import BaseModel, register_model
[docs]@register_model("prone")
class ProNE(BaseModel):
r"""The ProNE model from the `"ProNE: Fast and Scalable Network Representation Learning"
<https://www.ijcai.org/Proceedings/2019/0594.pdf>`_ paper.
Args:
hidden_size (int) : The dimension of node representation.
step (int) : The number of items in the chebyshev expansion.
mu (float) : Parameter in ProNE.
theta (float) : Parameter in ProNE.
"""
[docs] @staticmethod
def add_args(parser):
"""Add model-specific arguments to the parser."""
# fmt: off
parser.add_argument("--step", type=int, default=5,
help="Number of items in the chebyshev expansion")
parser.add_argument("--mu", type=float, default=0.2)
parser.add_argument("--theta", type=float, default=0.5)
# fmt: on
[docs] @classmethod
def build_model_from_args(cls, args):
return cls(args.hidden_size, args.step, args.mu, args.theta)
def __init__(self, dimension, step, mu, theta):
super(ProNE, self).__init__()
self.dimension = dimension
self.step = step
self.mu = mu
self.theta = theta
[docs] def train(self, G):
self.num_node = G.number_of_nodes()
self.matrix0 = sp.csr_matrix(nx.adjacency_matrix(G))
features_matrix = self._pre_factorization(self.matrix0, self.matrix0)
embeddings_matrix = self._chebyshev_gaussian(self.matrix0, features_matrix, self.step, self.mu, self.theta)
self.embeddings = embeddings_matrix
return self.embeddings
def _get_embedding_rand(self, matrix):
# Sparse randomized tSVD for fast embedding
smat = sp.csc_matrix(matrix) # convert to sparse CSC format
U, Sigma, VT = randomized_svd(smat, n_components=self.dimension, n_iter=5, random_state=None)
U = U * np.sqrt(Sigma)
U = preprocessing.normalize(U, "l2")
return U
def _get_embedding_dense(self, matrix, dimension):
# get dense embedding via SVD
U, s, Vh = linalg.svd(matrix, full_matrices=False, check_finite=False, overwrite_a=True)
U = np.array(U)
U = U[:, :dimension]
s = s[:dimension]
s = np.sqrt(s)
U = U * s
U = preprocessing.normalize(U, "l2")
return U
def _pre_factorization(self, tran, mask):
# Network Embedding as Sparse Matrix Factorization
l1 = 0.75
C1 = preprocessing.normalize(tran, "l1")
neg = np.array(C1.sum(axis=0))[0] ** l1
neg = neg / neg.sum()
neg = sp.diags(neg, format="csr")
neg = mask.dot(neg)
C1.data[C1.data <= 0] = 1
neg.data[neg.data <= 0] = 1
C1.data = np.log(C1.data)
neg.data = np.log(neg.data)
C1 -= neg
F = C1
features_matrix = self._get_embedding_rand(F)
return features_matrix
def _chebyshev_gaussian(self, A, a, order=5, mu=0.5, s=0.2, plus=False, nn=False):
# NE Enhancement via Spectral Propagation
num_node = a.shape[0]
if order == 1:
return a
A = sp.eye(num_node) + A
DA = preprocessing.normalize(A, norm="l1")
L = sp.eye(num_node) - DA
M = L - mu * sp.eye(num_node)
Lx0 = a
Lx1 = M.dot(a)
Lx1 = 0.5 * M.dot(Lx1) - a
conv = iv(0, s) * Lx0
conv -= 2 * iv(1, s) * Lx1
for i in range(2, order):
Lx2 = M.dot(Lx1)
Lx2 = (M.dot(Lx2) - 2 * Lx1) - Lx0
# Lx2 = 2*L.dot(Lx1) - Lx0
if i % 2 == 0:
conv += 2 * iv(i, s) * Lx2
else:
conv -= 2 * iv(i, s) * Lx2
Lx0 = Lx1
Lx1 = Lx2
del Lx2
emb = mm = conv
if not plus:
mm = A.dot(a - conv)
if not nn:
emb = self._get_embedding_dense(mm, self.dimension)
return emb