code: def make_outliers(
      n_matrices, mean, sigma, outlier_coeff=10, random_state=None
  ):
      """Generate a set of outlier points.
  
      Simulate data points that are outliers for a given Riemannian Gaussian
      distribution with fixed mean and dispersion.
  
      Parameters
      ----------
      n_matrices : int
          How many matrices to generate.
      mean : ndarray, shape (n_dim, n_dim)
          Center of the Riemannian Gaussian distribution.
      sigma : float
          Dispersion of the Riemannian Gaussian distribution.
      outlier_coeff: float, default=10
          Coefficient determining how to define an outlier data point, i.e. how
          many times the sigma parameter its distance to the mean should be.
      random_state : int, RandomState instance or None, default=None
          Pass an int for reproducible output across multiple function calls.
  
      Returns
      -------
      outliers : ndarray, shape (n_matrices, n_dim, n_dim)
          Set of simulated outlier matrix.
  
      Notes
      -----
      .. versionadded:: 0.3
      """
  
      n_dim = mean.shape[1]
      mean_sqrt = sqrtm(mean)
  
      outliers = np.zeros((n_matrices, n_dim, n_dim))
      for i in range(n_matrices):
          Oi = generate_random_spd_matrix(
              n_dim=n_dim, random_state=random_state
          )
          epsilon_num = outlier_coeff * sigma * n_dim
          epsilon_den = distance_riemann(
              Oi, np.eye(n_dim), squared=True
          )
          epsilon = np.sqrt(epsilon_num / epsilon_den)
          outliers[i] = mean_sqrt @ powm(Oi, epsilon) @ mean_sqrt
  
      return outliers
  
file_path: pyRiemann/pyriemann/datasets/simulated.py
imports: import numpy
  from sklearn.utils.validation import check_random_state
  from ..utils.mean import mean_riemann
  from ..utils.distance import distance_riemann
  from ..utils.base import invsqrtm, powm, sqrtm, expm
  from .sampling import generate_random_spd_matrix, sample_gaussian_spd
  from ..transfer import encode_domains
  from ..utils import deprecated
label_desc: Use image node_id 5 for calling a global function with example usage: make_outliers(n_matrices, mean, sigma, outlier_coeff, random_state) and returns: outliers