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.
code: def __init__(self, space):
      self.space = space
  
      self.optimizer = GradientDescent()
  
      self.estimate_ = None
  
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 2 to create a new ExponentialBarycenter object from inherited base classes: BaseEstimator with example: obj = ExponentialBarycenter(space)