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: Interface for instantiating proper algorithm.
docstr_tok: ["Interface","for","instantiating","proper","algorithm","."]
code: def __new__(cls, space):
      """Interface for instantiating proper algorithm."""
      if isinstance(space, Euclidean):
          return LinearMean(space)
  
      return super().__new__(cls)
  
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 1 for calling the ExponentialBarycenter obj's underlying member method code with example usage: obj.__new__(cls, space) and returns: super, LinearMean