sklearn.manifold.LocallyLinearEmbedding
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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)
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Locally Linear Embedding
Read more in the User Guide.
Parameters: |
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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’) -
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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' -
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 or None, optional (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: |
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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). |
[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. |
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__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=None)
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fit(X, y=None)
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Compute the embedding vectors for data X
Parameters: |
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X : array-like of shape [n_samples, n_features] -
training set. -
y : Ignored |
Returns: |
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self : returns an instance of self. |
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fit_transform(X, y=None)
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Compute the embedding vectors for data X and transform X.
Parameters: |
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X : array-like of shape [n_samples, n_features] -
training set. -
y : Ignored |
Returns: |
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X_new : array-like, shape (n_samples, n_components) |
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get_params(deep=True)
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Get parameters for this estimator.
Parameters: |
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deep : boolean, optional -
If True, will return the parameters for this estimator and contained subobjects that are estimators. |
Returns: |
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params : mapping of string to any -
Parameter names mapped to their values. |
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set_params(**params)
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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.
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transform(X)
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Transform new points into embedding space.
Parameters: |
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X : array-like, shape = [n_samples, n_features] |
Returns: |
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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