class_docstr: Isomap Embedding
  
  Non-linear dimensionality reduction through Isometric Mapping
  
  Read more in the :ref:`User Guide <isomap>`.
  
  Parameters
  ----------
  n_neighbors : integer
      number of neighbors to consider for each point.
  
  n_components : integer
      number of coordinates for the manifold
  
  eigen_solver : ['auto'|'arpack'|'dense']
      'auto' : Attempt to choose the most efficient solver
      for the given problem.
  
      'arpack' : Use Arnoldi decomposition to find the eigenvalues
      and eigenvectors.
  
      'dense' : Use a direct solver (i.e. LAPACK)
      for the eigenvalue decomposition.
  
  tol : float
      Convergence tolerance passed to arpack or lobpcg.
      not used if eigen_solver == 'dense'.
  
  max_iter : integer
      Maximum number of iterations for the arpack solver.
      not used if eigen_solver == 'dense'.
  
  path_method : string ['auto'|'FW'|'D']
      Method to use in finding shortest path.
  
      'auto' : attempt to choose the best algorithm automatically.
  
      'FW' : Floyd-Warshall algorithm.
  
      'D' : Dijkstra's algorithm.
  
  neighbors_algorithm : string ['auto'|'brute'|'kd_tree'|'ball_tree']
      Algorithm to use for nearest neighbors search,
      passed to neighbors.NearestNeighbors instance.
  
  n_jobs : int, optional (default = 1)
      The number of parallel jobs to run.
      If ``-1``, then the number of jobs is set to the number of CPU cores.
  
  Attributes
  ----------
  embedding_ : array-like, shape (n_samples, n_components)
      Stores the embedding vectors.
  
  kernel_pca_ : object
      `KernelPCA` object used to implement the embedding.
  
  training_data_ : array-like, shape (n_samples, n_features)
      Stores the training data.
  
  nbrs_ : sklearn.neighbors.NearestNeighbors instance
      Stores nearest neighbors instance, including BallTree or KDtree
      if applicable.
  
  dist_matrix_ : array-like, shape (n_samples, n_samples)
      Stores the geodesic distance matrix of training data.
  
  References
  ----------
  
  .. [1] Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric
         framework for nonlinear dimensionality reduction. Science 290 (5500)
docstr: Compute the reconstruction error for the embedding.
  
  Returns
  -------
  reconstruction_error : float
  
  Notes
  -------
  The cost function of an isomap embedding is
  
  ``E = frobenius_norm[K(D) - K(D_fit)] / n_samples``
  
  Where D is the matrix of distances for the input data X,
  D_fit is the matrix of distances for the output embedding X_fit,
  and K is the isomap kernel:
  
  ``K(D) = -0.5 * (I - 1/n_samples) * D^2 * (I - 1/n_samples)``
docstr_tok: ["Compute","the","reconstruction","error","for","the","embedding",".","Returns","--","--","--","-","reconstruction_error",":","float","Notes","--","--","--","-","The","cost","function","of","an","isomap","embedding","is","``","E","=","frobenius_norm","[","K","(","D",")","-","K","(","D_fit",")","]","\/","n_samples","``","Where","D","is","the","matrix","of","distances","for","the","input","data","X",",","D_fit","is","the","matrix","of","distances","for","the","output","embedding","X_fit",",","and","K","is","the","isomap","kernel",":","``","K","(","D",")","=","-0.5","*","(","I","-","1\/n_samples",")","*","D^2","*","(","I","-","1\/n_samples",")","``"]
code: def reconstruction_error(self):
      """Compute the reconstruction error for the embedding.
  
      Returns
      -------
      reconstruction_error : float
  
      Notes
      -------
      The cost function of an isomap embedding is
  
      ``E = frobenius_norm[K(D) - K(D_fit)] / n_samples``
  
      Where D is the matrix of distances for the input data X,
      D_fit is the matrix of distances for the output embedding X_fit,
      and K is the isomap kernel:
  
      ``K(D) = -0.5 * (I - 1/n_samples) * D^2 * (I - 1/n_samples)``
      """
      G = -0.5 * self.dist_matrix_**2
      G_center = KernelCenterer().fit_transform(G)
      evals = self.kernel_pca_.lambdas_
      return (
          np.sqrt(np.sum(G_center**2) - np.sum(evals**2))
          / G.shape[0]
      )
  
file_path: catboost/contrib/python/scikit-learn/py2/sklearn/manifold/isomap.py
imports: import numpy
  from ..base import BaseEstimator, TransformerMixin
  from ..neighbors import NearestNeighbors, kneighbors_graph
  from ..utils import check_array
  from ..utils.graph import graph_shortest_path
  from ..decomposition import KernelPCA
  from ..preprocessing import KernelCenterer
label_desc: Use image node_id 3 for calling the Isomap obj's underlying member method code with example usage: obj.reconstruction_error() and returns: unknown