import numpy as np
import networkx as nx
from typing import Union
from scipy import sparse
from scipy.sparse import coo_matrix
from karateclub.estimator import Estimator
[docs]class TENE(Estimator):
r"""An implementation of `"TENE" <https://ieeexplore.ieee.org/document/8545577>`_
from the ICPR '18 paper "Enhanced Network Embedding with Text Information". The
procedure jointly factorizes the adjacency and node feature matrices using alternating
least squares.
Args:
dimensions (int): Number of embedding dimensions. Default is 32.
lower_control (float): Embedding score minimal value. Default is 10**-15.
alpha (float): Adjacency matrix regularization coefficient. Default is 0.1.
beta (float): Feature matrix regularization coefficient. Default is 0.1.
iterations (int): ALS iterations. Default is 200.
seed (int): Random seed value. Default is 42.
"""
def __init__(
self,
dimensions=32,
lower_control=10**-15,
alpha=0.1,
beta=0.1,
iterations=200,
seed=42,
):
self.dimensions = dimensions
self.lower_control = lower_control
self.alpha = alpha
self.beta = beta
self.iterations = iterations
self.seed = seed
def _init_weights(self):
"""
Setup basis and feature matrices.
"""
self._M = np.random.uniform(0, 1, (self._X.shape[0], self.dimensions))
self._U = np.random.uniform(0, 1, (self._X.shape[0], self.dimensions))
self._Q = np.random.uniform(0, 1, (self._X.shape[0], self.dimensions))
self._V = np.random.uniform(0, 1, (self._T.shape[1], self.dimensions))
self._C = np.random.uniform(0, 1, (self.dimensions, self.dimensions))
def _update_M(self):
"""
Update node bases.
"""
enum = self._X.dot(self._U)
denom = self._M.dot(self._U.T.dot(self._U))
self._M = np.multiply(self._M, enum / denom)
self._M[self._M < self.lower_control] = self.lower_control
def _update_V(self):
"""
Update node features.
"""
enum = self._T.T.dot(self._Q)
denom = self._V.dot(self._Q.T.dot(self._Q))
self._V = np.multiply(self._V, enum / denom)
self._V[self._V < self.lower_control] = self.lower_control
def _update_C(self):
"""
Update transformation matrix.
"""
enum = self._Q.T.dot(self._U)
denom = self._C.dot(self._U.T.dot(self._U))
self._C = np.multiply(self._C, enum / denom)
self._C[self._C < self.lower_control] = self.lower_control
def _update_U(self):
"""
Update features.
"""
enum = self._X.T.dot(self._M) + self.alpha * self._Q.dot(self._C)
denom = self._U.dot(
(self._M.T.dot(self._M) + self.alpha * self._C.T.dot(self._C))
)
self._U = np.multiply(self._U, enum / denom)
self._U[self._U < self.lower_control] = self.lower_control
def _update_Q(self):
"""
Update feature bases.
"""
enum = self.alpha * self._U.dot(self._C.T) + self.beta * self._T.dot(self._V)
denom = self.alpha * self._Q + self.beta * self._Q.dot(self._V.T.dot(self._V))
self._Q = np.multiply(self._Q, enum / denom)
self._Q[self._Q < self.lower_control] = self.lower_control
def _create_D_inverse(self, graph):
"""
Creating a sparse inverse degree matrix.
Arg types:
* **graph** *(NetworkX graph)* - The graph to be embedded.
Return types:
* **D_inverse** *(Scipy array)* - Diagonal inverse degree matrix.
"""
index = np.arange(graph.number_of_nodes())
values = np.array(
[1.0 / graph.degree[node] for node in range(graph.number_of_nodes())]
)
shape = (graph.number_of_nodes(), graph.number_of_nodes())
D_inverse = sparse.coo_matrix((values, (index, index)), shape=shape)
return D_inverse
def _create_base_matrix(self, graph):
"""
Creating a normalized adjacency matrix.
Return types:
* **A_hat* - Normalized adjacency matrix.
"""
A = nx.adjacency_matrix(graph, nodelist=range(graph.number_of_nodes()))
D_inverse = self._create_D_inverse(graph)
A_hat = D_inverse.dot(A)
return A_hat
[docs] def fit(self, graph: nx.classes.graph.Graph, T: Union[np.array, coo_matrix]):
"""
Fitting a TENE model.
Arg types:
* **graph** *(NetworkX graph)* - The graph to be embedded.
* **T** *(Scipy COO or Numpy array)* - The matrix of node features.
"""
self._set_seed()
graph = self._check_graph(graph)
self._X = self._create_base_matrix(graph)
self._T = T
self._init_weights()
for _ in range(self.iterations):
self._update_M()
self._update_V()
self._update_C()
self._update_U()
self._update_Q()
[docs] def get_embedding(self) -> np.array:
r"""Getting the node embedding.
Return types:
* **embedding** *(Numpy array)* - The embedding of nodes.
"""
embedding = np.concatenate([self._M, self._Q], axis=1)
return embedding