`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_neighborsint, default=5

number of neighbors to consider for each point.

n_componentsint, default=2

number of coordinates for the manifold

regfloat, default=1e-3

regularization constant, multiplies the trace of the local covariance matrix of the distances.

eigen_solver{‘auto’, ‘arpack’, ‘dense’}, default=’auto’

auto : algorithm will attempt to choose the best method for input data

arpackuse 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.
denseuse 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.

tolfloat, default=1e-6

Tolerance for ‘arpack’ method Not used if eigen_solver==’dense’.

max_iterint, 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_tolfloat, default=1e-4

Tolerance for Hessian eigenmapping method. Only used if method == 'hessian'

modified_tolfloat, 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 neighbors.NearestNeighbors instance

random_stateint, 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_jobsint or None, 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.

Attributes

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, _ = 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)

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.

fit(X, y=None)[source]¶

Compute the embedding vectors for data X

Parameters

Xarray-like of shape [n_samples, n_features]: training set.
yIgnored

Returns

selfreturns an instance of self.

fit_transform(X, y=None)[source]¶

Compute the embedding vectors for data X and transform X.

Parameters

Xarray-like of shape [n_samples, n_features]: training set.
yIgnored

Returns

X_newarray-like, shape (n_samples, n_components)

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters

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

Returns

paramsdict: 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 Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters