class_docstr: Locally Linear Embedding.
  
  Read more in the :ref:`User Guide <locally_linear_embedding>`.
  
  Parameters
  ----------
  n_neighbors : int, default=5
      Number of neighbors to consider for each point.
  
  n_components : int, default=2
      Number of coordinates for the manifold.
  
  reg : float, default=1e-3
      Regularization constant, multiplies the trace of the local covariance
      matrix of the distances.
  
  eigen_solver : {'auto', 'arpack', 'dense'}, default='auto'
      The solver used to compute the eigenvectors. The available options are:
  
      - `'auto'` : algorithm will attempt to choose the best method for input
        data.
      - `'arpack'` : use arnoldi iteration in shift-invert mode. For this
        method, M may be a dense matrix, sparse matrix, or general linear
        operator.
      - `'dense'`  : use standard dense matrix operations for the eigenvalue
        decomposition. For this method, M must be an array or matrix type.
        This method should be avoided for large problems.
  
      .. warning::
         ARPACK can be unstable for some problems.  It is best to try several
         random seeds in order to check results.
  
  tol : float, default=1e-6
      Tolerance for 'arpack' method
      Not used if eigen_solver=='dense'.
  
  max_iter : int, default=100
      Maximum number of iterations for the arpack solver.
      Not used if eigen_solver=='dense'.
  
  method : {'standard', 'hessian', 'modified', 'ltsa'}, default='standard'
      - `standard`: use the standard locally linear embedding algorithm. see
        reference [1]_
      - `hessian`: use the Hessian eigenmap method. This method requires
        ``n_neighbors > n_components * (1 + (n_components + 1) / 2``. see
        reference [2]_
      - `modified`: use the modified locally linear embedding algorithm.
        see reference [3]_
      - `ltsa`: use local tangent space alignment algorithm. see
        reference [4]_
  
  hessian_tol : float, default=1e-4
      Tolerance for Hessian eigenmapping method.
      Only used if ``method == 'hessian'``.
  
  modified_tol : float, default=1e-12
      Tolerance for modified LLE method.
      Only used if ``method == 'modified'``.
  
  neighbors_algorithm : {'auto', 'brute', 'kd_tree', 'ball_tree'},                           default='auto'
      Algorithm to use for nearest neighbors search, passed to
      :class:`~sklearn.neighbors.NearestNeighbors` instance.
  
  random_state : int, RandomState instance, default=None
      Determines the random number generator when
      ``eigen_solver`` == 'arpack'. Pass an int for reproducible results
      across multiple function calls. See :term:`Glossary <random_state>`.
  
  n_jobs : int or None, default=None
      The number of parallel jobs to run.
      ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
      ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
      for more details.
  
  Attributes
  ----------
  embedding_ : array-like, shape [n_samples, n_components]
      Stores the embedding vectors
  
  reconstruction_error_ : float
      Reconstruction error associated with `embedding_`
  
  n_features_in_ : int
      Number of features seen during :term:`fit`.
  
      .. versionadded:: 0.24
  
  feature_names_in_ : ndarray of shape (`n_features_in_`,)
      Names of features seen during :term:`fit`. Defined only when `X`
      has feature names that are all strings.
  
      .. versionadded:: 1.0
  
  nbrs_ : NearestNeighbors object
      Stores nearest neighbors instance, including BallTree or KDtree
      if applicable.
  
  See Also
  --------
  SpectralEmbedding : Spectral embedding for non-linear dimensionality
      reduction.
  TSNE : Distributed Stochastic Neighbor Embedding.
  
  References
  ----------
  
  .. [1] Roweis, S. & Saul, L. Nonlinear dimensionality reduction
      by locally linear embedding.  Science 290:2323 (2000).
  .. [2] Donoho, D. & Grimes, C. Hessian eigenmaps: Locally
      linear embedding techniques for high-dimensional data.
      Proc Natl Acad Sci U S A.  100:5591 (2003).
  .. [3] `Zhang, Z. & Wang, J. MLLE: Modified Locally Linear
      Embedding Using Multiple Weights.
      <https://citeseerx.ist.psu.edu/doc_view/pid/0b060fdbd92cbcc66b383bcaa9ba5e5e624d7ee3>`_
  .. [4] Zhang, Z. & Zha, H. Principal manifolds and nonlinear
      dimensionality reduction via tangent space alignment.
      Journal of Shanghai Univ.  8:406 (2004)
  
  Examples
  --------
  >>> from sklearn.datasets import load_digits
  >>> from sklearn.manifold import LocallyLinearEmbedding
  >>> X, _ = load_digits(return_X_y=True)
  >>> X.shape
  (1797, 64)
  >>> embedding = LocallyLinearEmbedding(n_components=2)
  >>> X_transformed = embedding.fit_transform(X[:100])
  >>> X_transformed.shape
  (100, 2)
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docstr: Compute the embedding vectors for data X and transform X.
  
  Parameters
  ----------
  X : array-like of shape (n_samples, n_features)
      Training set.
  
  y : Ignored
      Not used, present here for API consistency by convention.
  
  Returns
  -------
  X_new : array-like, shape (n_samples, n_components)
      Returns the instance itself.
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code: def fit_transform(self, X, y=None):
      """Compute the embedding vectors for data X and transform X.
  
      Parameters
      ----------
      X : array-like of shape (n_samples, n_features)
          Training set.
  
      y : Ignored
          Not used, present here for API consistency by convention.
  
      Returns
      -------
      X_new : array-like, shape (n_samples, n_components)
          Returns the instance itself.
      """
      self._fit_transform(X)
      return self.embedding_
  
imports: from numbers import Integral, Real
  import numpy
  from scipy.linalg import eigh, qr, solve, svd
  from scipy.sparse import csr_matrix, eye
  from scipy.sparse.linalg import eigsh
  from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin, _fit_context, _UnstableArchMixin
  from ..neighbors import NearestNeighbors
  from ..utils import check_array, check_random_state
  from ..utils._arpack import _init_arpack_v0
  from ..utils._param_validation import Interval, StrOptions
  from ..utils.extmath import stable_cumsum
  from ..utils.validation import FLOAT_DTYPES, check_is_fitted
label_desc: Use image node_id 4 for calling the LocallyLinearEmbedding obj's underlying member method code with example usage: obj.fit_transform(X, y) and returns: self