Source code for karateclub.node_embedding.structural.graphwave

import pygsp
import numpy as np
import networkx as nx
from karateclub.estimator import Estimator

[docs]class GraphWave(Estimator): r"""An implementation of `"GraphWave" <https://dl.acm.org/citation.cfm?id=2806512>`_ from the KDD '18 paper "Learning Structural Node Embeddings Via Diffusion Wavelets". The procedure first calculates the graph wavelets using a heat kernel. The wavelets are treated as probability distributions over nodes from a source node. Using these the characteristic function is evaluated at certain gird points to learn structural node embeddings of the vertices. Args: sample_number (int): Number of evaluation points. Default is 200. step_size (float): Grid point step size. Default is 0.1. heat_coefficient (float): Heat kernel coefficient. Default is 1.0. approximation (int): Chebyshev polynomial order. Default is 100. mechanism (str): Wavelet calculation method one of: (:obj:`"exact"`, :obj:`"approximate"`). Default is 'approximate'. switch (int): Vertex cardinality when the wavelet calculation method switches to approximation. Default is 1000. seed (int): Random seed value. Default is 42. """ def __init__( self, sample_number: int = 200, step_size: float = 0.1, heat_coefficient: float = 1.0, approximation: int = 100, mechanism: str = "approximate", switch: int = 1000, seed: int = 42, ): self.sample_number = sample_number self.step_size = step_size self.heat_coefficient = heat_coefficient self.approximation = approximation self.mechanism = mechanism self.switch = switch self.seed = seed def _create_evaluation_points(self): """ Calculating the grid points. """ self._steps = [x * self.step_size for x in range(self.sample_number)] def _check_size(self, graph): """ Checking the size of the target graph. Switching based on size and settings. Arg types: * **graph** *(NetworkX graph)* - The graph being embedded. """ self._number_of_nodes = graph.number_of_nodes() if self._number_of_nodes > self.switch: self.mechanism = "approximate" def _single_wavelet_generator(self, node): """ Calculating the characteristic function for a given node, using the eigen decomposition. Arg types: * **node** *(int)* - The node being embedded. Return types: * **wavelet_coefficients** *(Numpy array)* - The wavelet representation of the node. """ impulse = np.zeros((self._number_of_nodes)) impulse[node] = 1.0 diags = np.diag(np.exp(-self.heat_coefficient * self._eigen_values)) eigen_diag = np.dot(self._eigen_vectors, diags) waves = np.dot(eigen_diag, np.transpose(self._eigen_vectors)) wavelet_coefficients = np.dot(waves, impulse) return wavelet_coefficients def _exact_wavelet_calculator(self): """ Calculates the structural role embedding using the exact eigenvalue decomposition. """ self._real_and_imaginary = [] for node in range(self._number_of_nodes): wave = self._single_wavelet_generator(node) wavelet_coefficients = [ np.mean(np.exp(wave * 1.0 * step * 1j)) for step in self._steps ] self._real_and_imaginary.append(wavelet_coefficients) self._real_and_imaginary = np.array(self._real_and_imaginary) def _exact_structural_wavelet_embedding(self): """ Calculates the eigenvectors, eigenvalues and an exact embedding is created. """ self._G.compute_fourier_basis() self._eigen_values = self._G.e / max(self._G.e) self._eigen_vectors = self._G.U self._exact_wavelet_calculator() def _approximate_wavelet_calculator(self): """ Given the Chebyshev polynomial and graph the approximate embedding is calculated. """ self._real_and_imaginary = [] for node in range(self._number_of_nodes): impulse = np.zeros((self._number_of_nodes)) impulse[node] = 1 wave_coeffs = pygsp.filters.approximations.cheby_op( self._G, self._chebyshev, impulse ) real_imag = [ np.mean(np.exp(wave_coeffs * 1 * step * 1j)) for step in self._steps ] self._real_and_imaginary.append(real_imag) self._real_and_imaginary = np.array(self._real_and_imaginary) def _approximate_structural_wavelet_embedding(self): """ Estimating the largest eigenvalue. Setting up the heat filter and the Cheybshev polynomial. Using the approximate wavelet calculator method. """ self._G.estimate_lmax() self._heat_filter = pygsp.filters.Heat(self._G, tau=[self.heat_coefficient]) self._chebyshev = pygsp.filters.approximations.compute_cheby_coeff( self._heat_filter, m=self.approximation ) self._approximate_wavelet_calculator()
[docs] def fit(self, graph: nx.classes.graph.Graph): """ Fitting a GraphWave model. Arg types: * **graph** *(NetworkX graph)* - The graph to be embedded. """ self._set_seed() graph = self._check_graph(graph) self._create_evaluation_points() self._check_size(graph) self._G = pygsp.graphs.Graph(nx.adjacency_matrix(graph)) if self.mechanism == "exact": self._exact_structural_wavelet_embedding() elif self.mechanism == "approximate": self._approximate_structural_wavelet_embedding() else: raise NameError("Unknown method.")
[docs] def get_embedding(self) -> np.array: r"""Getting the node embedding. Return types: * **embedding** *(Numpy array)* - The embedding of nodes. """ embedding = [self._real_and_imaginary.real, self._real_and_imaginary.imag] embedding = np.concatenate(embedding, axis=1) return embedding