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=1)

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, 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_vectors_ : array-like, shape [n_components, n_samples]

Stores the embedding vectors

reconstruction_error_ : float

Reconstruction error associated with embedding_vectors_

nbrs_ : NearestNeighbors object

Stores nearest neighbors instance, including BallTree or KDtree if applicable.

References

[R189]

Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000).

[R190]

Donoho, D. & Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci U S A. 100:5591 (2003).

[R191]

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

[R192]

Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004)

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=1)

fit(X, y=None)

Compute the embedding vectors for data X

Parameters:

X : array-like of shape [n_samples, n_features]

training set.

y: Ignored. :

Returns:

self : returns an instance of self.

fit_transform(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. :

Returns:

X_new : array-like, shape (n_samples, n_components)

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params : mapping of string to any

Parameter names mapped to their values.

set_params(**params)

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)

Transform new points into embedding space.

Parameters:X : array-like, shape = [n_samples, n_features] Returns: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)

Examples using sklearn.manifold.LocallyLinearEmbedding

Visualizing the stock market structure

Comparison of Manifold Learning methods

Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…

Manifold Learning methods on a severed sphere