class_docstr: Gaussian mixture model (GMM).
  
  Parameters
  ----------
  space : Manifold
      Equipped manifold.
  means : array-like, shape=[n_gaussians, dim]
      Means of each component of the GMM.
  variances : array-like, shape=[n_gaussians,]
      Variances of each component of the GMM.
  
  Attributes
  ----------
  normalization_factor_var : array-like, shape=[n_variances,]
      Array of computed normalization factor.
  variances_range : array-like, shape=[n_variances,]
      Array of standard deviations.
  phi_inv_var : array-like, shape=[n_variances,]
      Array of the computed inverse of a function phi
      whose expression is closed-form
      :math:`\sigma\mapsto \sigma^3 \times \frac{d}
      {\mathstrut d\sigma}\log \zeta_m(\sigma)`
      where :math:`\sigma` denotes the variance
      and :math:`\zeta` the normalization coefficient
      and :math:`m` the dimension.
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code: def __init__(
      self,
      space,
      means=None,
      variances=None,
      zeta_lower_bound=5e-1,
      zeta_upper_bound=2.0,
      zeta_step=0.01,
  ):
      self.space = space
      self.means = means
      self.variances = variances
  
      self.zeta_lower_bound = zeta_lower_bound
      self.zeta_upper_bound = zeta_upper_bound
      self.zeta_step = zeta_step
  
      (
          self.variances_range,
          self.normalization_factor_var,
          self.phi_inv_var,
      ) = self._normalization_factor_init()
  
imports: import logging
  from sklearn.base import BaseEstimator, ClusterMixin
  import geomstats.backend
  from geomstats.learning._template import TransformerMixin
  from geomstats.learning.frechet_mean import FrechetMean, variance
  from geomstats.learning.kmeans import RiemannianKMeans
label_desc: Use image node_id 1 to create a new GaussianMixtureModel object  with example: obj = GaussianMixtureModel(space, means, variances, zeta_lower_bound, zeta_upper_bound, zeta_step)