`sklearn.manifold`.locally_linear_embedding¶

sklearn.manifold.locally_linear_embedding(X, n_neighbors, n_components, reg=0.001, eigen_solver='auto', tol=1e-06, max_iter=100, method='standard', hessian_tol=0.0001, modified_tol=1e-12, random_state=None, n_jobs=None)[source]¶

Perform a Locally Linear Embedding analysis on the data.

Read more in the User Guide.

Parameters

X{array-like, NearestNeighbors}

Sample data, shape = (n_samples, n_features), in the form of a numpy array or a NearestNeighbors object.

n_neighborsinteger

number of neighbors to consider for each point.

n_componentsinteger

number of coordinates for the manifold.

regfloat

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

eigen_solverstring, {‘auto’, ‘arpack’, ‘dense’}

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, optional

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

max_iterinteger

maximum number of iterations for the arpack solver.

method{‘standard’, ‘hessian’, ‘modified’, ‘ltsa’}

standarduse the standard locally linear embedding algorithm.: see reference [1]
hessianuse the Hessian eigenmap method. This method requires: n_neighbors > n_components * (1 + (n_components + 1) / 2. see reference [2]
modifieduse the modified locally linear embedding algorithm.: see reference [3]
ltsause local tangent space alignment algorithm: see reference [4]

hessian_tolfloat, optional

Tolerance for Hessian eigenmapping method. Only used if method == ‘hessian’

modified_tolfloat, optional

Tolerance for modified LLE method. Only used if method == ‘modified’

random_stateint, 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 solver == ‘arpack’.

n_jobsint or None, optional (default=None)

The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Returns

Yarray-like, shape [n_samples, n_components]: Embedding vectors.
squared_errorfloat: Reconstruction error for the embedding vectors. Equivalent to norm(Y - W Y, 'fro')**2, where W are the reconstruction weights.

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)

sklearn.manifold.locally_linear_embedding¶

`sklearn.manifold`.locally_linear_embedding¶