class_docstr: Empirical exponential barycenter for matrix groups.
  
  Parameters
  ----------
  space : LieGroup
      Lie group instance on which the data lie.
  
  Attributes
  ----------
  estimate_ : array-like, shape=[dim, dim]
      If fit, exponential barycenter.
docstr: Compute the empirical weighted exponential barycenter.
  
  Parameters
  ----------
  X : array-like, shape=[n_samples, dim, dim]
      Training input samples.
  y : None
      Target values. Ignored.
  weights : array-like, shape=[n_samples,]
      Weights associated to the samples.
      Optional, default: None, in which case it is equally weighted.
  
  Returns
  -------
  self : object
      Returns self.
docstr_tok: ["Compute","the","empirical","weighted","exponential","barycenter",".","Parameters","--","--","--","--","--","X",":","array-like",",","shape=","[","n_samples",",","dim",",","dim","]","Training","input","samples",".","y",":","None","Target","values",".","Ignored",".","weights",":","array-like",",","shape=","[","n_samples",",","]","Weights","associated","to","the","samples",".","Optional",",","default",":","None",",","in","which","case","it","is","equally","weighted",".","Returns","--","--","--","-","self",":","object","Returns","self","."]
code: def fit(self, X, y=None, weights=None):
      """Compute the empirical weighted exponential barycenter.
  
      Parameters
      ----------
      X : array-like, shape=[n_samples, dim, dim]
          Training input samples.
      y : None
          Target values. Ignored.
      weights : array-like, shape=[n_samples,]
          Weights associated to the samples.
          Optional, default: None, in which case it is equally weighted.
  
      Returns
      -------
      self : object
          Returns self.
      """
      # TODO (nguigs): use closed form expression for special euclidean
      #  group as before PR #537
  
      self.estimate_ = self.optimizer.minimize(
          group=self.space,
          points=X,
          weights=weights,
      )
  
      return self
  
file_path: geomstats/geomstats/learning/exponential_barycenter.py
imports: import logging
  from sklearn.base import BaseEstimator
  import geomstats.backend
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.learning.frechet_mean import BaseGradientDescent, LinearMean
label_desc: Use image node_id 4 for calling the ExponentialBarycenter obj's underlying member method code with example usage: obj.fit(X, y, weights) and returns: self