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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=1)
[source] -
Perform a Locally Linear Embedding analysis on the data.
Read more in the User Guide.
Parameters: X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}
Sample data, shape = (n_samples, n_features), in the form of a numpy array, sparse array, precomputed tree, or 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
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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?}
- standard
: use the standard locally linear embedding algorithm.
see reference [R190]
hessian
: use the Hessian eigenmap method. This method requires
n_neighbors > n_components * (1 + (n_components + 1) / 2. see reference [R191]
modified
: use the modified locally linear embedding algorithm.
see reference [R192]
ltsa
: use local tangent space alignment algorithm
see reference [R193]
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: numpy.RandomState or int, optional :
The generator or seed used to determine the starting vector for arpack iterations. Defaults to numpy.random.
n_jobs : int, optional (default = 1)
The number of parallel jobs to run for neighbors search. If -1
, then the number of jobs is set to the number of CPU cores.
Returns:
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
[R190] |
(1, 2) Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000).
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[R191] |
(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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[R192] |
(1, 2) 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
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[R193] |
(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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