Hope Algorithm Implementation Question

[ahmedlebo]

In the paper:Asymmetric Transitivity Preserving Graph Embedding,the authors state that they will not calculate S in this part

so that in this algorithm, they do not explicitly perform the polynomial operation on adjacency matrix in Ml and Mg, but in the implementation the S matrix is calculated fully as this shows,

I can't understand it so anyone please could explain this to me

[ahmedlebo]

Does anyone share the same problem or has a different point of view or there something i am missing in the paper

[VaradScript]

It seems like you're trying to describe a Python implementation of a method for generating a target similarity matrix and performing a rescaled decomposition, likely for a graph embedding or matrix factorization task.

[VaradScript]

import numpy as np
import scipy.sparse as sps
from scipy.sparse.linalg import svds

class GraphEmbedding:
def init(self, dimensions):
self.dimensions = dimensions
self._left_embedding = None
self._right_embedding = None

def create_target(self, graph):
    """
    Creates a target similarity matrix for the given graph.
    
    Parameters:
    graph : networkx.Graph
        Input graph for which the similarity matrix is created.
    
    Returns:
    S : scipy.sparse.coo_matrix
        Target similarity matrix.
    """
    number_of_nodes = graph.number_of_nodes()
    A = nx.adjacency_matrix(graph, nodelist=range(number_of_nodes))
    S = sps.coo_matrix(A.dot(A), dtype=np.float32)
    return S

def do_rescaled_decomposition(self, S):
    """
    Performs Singular Value Decomposition (SVD) on the similarity matrix
    and rescales the results to compute embeddings.
    
    Parameters:
    S : scipy.sparse.coo_matrix
        Input similarity matrix.
    """
    U, sigmas, Vt = svds(S, k=int(self.dimensions / 2))
    sigmas = np.diagflat(np.sqrt(sigmas))
    self._left_embedding = np.dot(U, sigmas)
    self._right_embedding = np.dot(Vt.T, sigmas)