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: Transform X.
  
  This is implemented by linking the points X into the graph of geodesic
  distances of the training data. First the `n_neighbors` nearest
  neighbors of X are found in the training data, and from these the
  shortest geodesic distances from each point in X to each point in
  the training data are computed in order to construct the kernel.
  The embedding of X is the projection of this kernel onto the
  embedding vectors of the training set.
  
  Parameters
  ----------
  X: array-like, shape (n_samples, n_features)
  
  Returns
  -------
  X_new: array-like, shape (n_samples, n_components)
docstr_tok: ["Transform","X",".","This","is","implemented","by","linking","the","points","X","into","the","graph","of","geodesic","distances","of","the","training","data",".","First","the","`","n_neighbors","`","nearest","neighbors","of","X","are","found","in","the","training","data",",","and","from","these","the","shortest","geodesic","distances","from","each","point","in","X","to","each","point","in","the","training","data","are","computed","in","order","to","construct","the","kernel",".","The","embedding","of","X","is","the","projection","of","this","kernel","onto","the","embedding","vectors","of","the","training","set",".","Parameters","--","--","--","--","--","X",":","array-like",",","shape","(","n_samples",",","n_features",")","Returns","--","--","--","-","X_new",":","array-like",",","shape","(","n_samples",",","n_components",")"]
code: def transform(self, X):
      """Transform X.
  
      This is implemented by linking the points X into the graph of geodesic
      distances of the training data. First the `n_neighbors` nearest
      neighbors of X are found in the training data, and from these the
      shortest geodesic distances from each point in X to each point in
      the training data are computed in order to construct the kernel.
      The embedding of X is the projection of this kernel onto the
      embedding vectors of the training set.
  
      Parameters
      ----------
      X: array-like, shape (n_samples, n_features)
  
      Returns
      -------
      X_new: array-like, shape (n_samples, n_components)
      """
      X = check_array(X)
      distances, indices = self.nbrs_.kneighbors(
          X, return_distance=True
      )
  
      # Create the graph of shortest distances from X to self.training_data_
      # via the nearest neighbors of X.
      # This can be done as a single array operation, but it potentially
      # takes a lot of memory.  To avoid that, use a loop:
      G_X = np.zeros((X.shape[0], self.training_data_.shape[0]))
      for i in range(X.shape[0]):
          G_X[i] = np.min(
              self.dist_matrix_[indices[i]] + distances[i][:, None], 0
          )
  
      G_X **= 2
      G_X *= -0.5
  
      return self.kernel_pca_.transform(G_X)
  
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 6 for calling the Isomap obj's underlying member method code with example usage: obj.transform(X) and returns: self