# sklearn.manifold.LocallyLinearEmbedding¶

class sklearn.manifold.LocallyLinearEmbedding(n_neighbors=5, n_components=2, reg=0.001, eigen_solver=’auto’, tol=1e-06, max_iter=100, method=’standard’, hessian_tol=0.0001, modified_tol=1e-12, neighbors_algorithm=’auto’, random_state=None, n_jobs=None)[source]

Locally Linear Embedding

Read more in the User Guide.

Parameters: n_neighbors : integer number of neighbors to consider for each point. n_components : integer number of coordinates for the manifold reg : float regularization constant, multiplies the trace of the local covariance matrix of the distances. eigen_solver : string, {‘auto’, ‘arpack’, ‘dense’} 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. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. 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. tol : float, optional Tolerance for ‘arpack’ method Not used if eigen_solver==’dense’. max_iter : integer maximum number of iterations for the arpack solver. Not used if eigen_solver==’dense’. method : string (‘standard’, ‘hessian’, ‘modified’ or ‘ltsa’) 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, optional Tolerance for Hessian eigenmapping method. Only used if method == 'hessian' modified_tol : float, optional Tolerance for modified LLE method. Only used if method == 'modified' neighbors_algorithm : string [‘auto’|’brute’|’kd_tree’|’ball_tree’] algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when eigen_solver == ‘arpack’. n_jobs : int or None, optional (default=None) The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details. embedding_ : array-like, shape [n_samples, n_components] Stores the embedding vectors reconstruction_error_ : float Reconstruction error associated with embedding_ nbrs_ : NearestNeighbors object Stores nearest neighbors instance, including BallTree or KDtree if applicable.

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. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382
 [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.shape
(1797, 64)
>>> embedding = LocallyLinearEmbedding(n_components=2)
>>> X_transformed = embedding.fit_transform(X[:100])
>>> X_transformed.shape
(100, 2)


Methods

 fit(X[, y]) Compute the embedding vectors for data X fit_transform(X[, y]) Compute the embedding vectors for data X and transform X. get_params([deep]) Get parameters for this estimator. set_params(**params) Set the parameters of this estimator. transform(X) Transform new points into embedding space.
__init__(n_neighbors=5, n_components=2, reg=0.001, eigen_solver=’auto’, tol=1e-06, max_iter=100, method=’standard’, hessian_tol=0.0001, modified_tol=1e-12, neighbors_algorithm=’auto’, random_state=None, n_jobs=None)[source]
fit(X, y=None)[source]

Compute the embedding vectors for data X

Parameters: X : array-like of shape [n_samples, n_features] training set. y : Ignored self : returns an instance of self.
fit_transform(X, y=None)[source]

Compute the embedding vectors for data X and transform X.

Parameters: X : array-like of shape [n_samples, n_features] training set. y : Ignored X_new : array-like, shape (n_samples, n_components)
get_params(deep=True)[source]

Get parameters for this estimator.

Parameters: deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators. params : mapping of string to any Parameter names mapped to their values.
set_params(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns: self
transform(X)[source]

Transform new points into embedding space.

Parameters: X : array-like, shape = [n_samples, n_features] X_new : array, shape = [n_samples, n_components]

Notes

Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs)