sklearn.manifold.locally_linear_embedding
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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]
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Perform a Locally Linear Embedding analysis on the data.
Read more in the User Guide.
Parameters: |
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X : {array-like, NearestNeighbors} -
Sample data, shape = (n_samples, n_features), in the form of a numpy array or a NearestNeighbors object. -
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. -
method : {‘standard’, ‘hessian’, ‘modified’, ‘ltsa’} -
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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’ -
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 solver == ‘arpack’. -
n_jobs : int 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: |
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Y : array-like, shape [n_samples, n_components] -
Embedding vectors. -
squared_error : float -
Reconstruction error for the embedding vectors. Equivalent to norm(Y - W Y, 'fro')**2 , where W are the reconstruction weights. |
References
[1] |
(1, 2) Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000).
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[2] |
(1, 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).
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[4] |
(1, 2) Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004)
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Examples using sklearn.manifold.locally_linear_embedding