class_docstr: DGCF is a disentangled representation enhanced matrix factorization model.
  The interaction matrix of :math:`n_{users} \times n_{items}` is decomposed to :math:`n_{factors}` intent graph,
  we carefully design the data interface and use sparse tensor to train and test efficiently.
  We implement the model following the original author with a pairwise training mode.
code: def _create_distance_correlation(self, X1, X2):
      def _create_centered_distance(X):
          """
          X: (batch_size, dim)
          return: X - E(X)
          """
          # calculate the pairwise distance of X
          # .... A with the size of [batch_size, embed_size/n_factors]
          # .... D with the size of [batch_size, batch_size]
          r = torch.sum(X * X, dim=1, keepdim=True)
          # (N, 1)
          # (x^2 - 2xy + y^2) -> l2 distance between all vectors
          value = r - 2 * torch.mm(X, X.T) + r.T
          zero_value = torch.zeros_like(value)
          value = torch.where(value > 0.0, value, zero_value)
          D = torch.sqrt(value + 1e-8)
  
          # # calculate the centered distance of X
          # # .... D with the size of [batch_size, batch_size]
          # matrix - average over row - average over col + average over matrix
          D = (
              D
              - torch.mean(D, dim=0, keepdim=True)
              - torch.mean(D, dim=1, keepdim=True)
              + torch.mean(D)
          )
          return D
  
      def _create_distance_covariance(D1, D2):
          # calculate distance covariance between D1 and D2
          n_samples = float(D1.size(0))
          value = torch.sum(D1 * D2) / (n_samples * n_samples)
          zero_value = torch.zeros_like(value)
          value = torch.where(value > 0.0, value, zero_value)
          dcov = torch.sqrt(value + 1e-8)
          return dcov
  
      D1 = _create_centered_distance(X1)
      D2 = _create_centered_distance(X2)
  
      dcov_12 = _create_distance_covariance(D1, D2)
      dcov_11 = _create_distance_covariance(D1, D1)
      dcov_22 = _create_distance_covariance(D2, D2)
  
      # calculate the distance correlation
      value = dcov_11 * dcov_22
      zero_value = torch.zeros_like(value)
      value = torch.where(value > 0.0, value, zero_value)
      dcor = dcov_12 / (torch.sqrt(value) + 1e-10)
      return dcor
  
imports: import random
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  from torch.autograd import Variable
  from recbole.model.abstract_recommender import GeneralRecommender
  from recbole.model.init import xavier_normal_initialization
  from recbole.model.loss import BPRLoss, EmbLoss
  from recbole.utils import InputType
label_desc: Use image node_id 8 for calling the DGCF obj's underlying member method code with example usage: obj._create_distance_correlation(X1, X2) and returns: dcor, D, dcov