8.15.1. sklearn.manifold.LocallyLinearEmbedding¶
- class sklearn.manifold.LocallyLinearEmbedding(n_neighbors=5, out_dim=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')¶
Locally Linear Embedding
Parameters : n_neighbors : integer
number of neighbors to consider for each point.
out_dim : 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.
- 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’]
- standard : use the standard locally linear embedding algorithm.
see reference [1]
- hessian : use the Hessian eigenmap method. This method requires
n_neighbors > out_dim * (1 + (out_dim + 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
Attributes
embedding_vectors_ array-like, shape [out_dim, n_samples] Stores the embedding vectors reconstruction_error_ float Reconstruction error associated with embedding_vectors_ nbrs_ NearestNeighbors object Stores nearest neighbors instance, including BallTree or KDtree if applicable. 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. set_params(**params) Set the parameters of the estimator. transform(X) Transform new points into embedding space. - __init__(n_neighbors=5, out_dim=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')¶
- fit(X, y=None)¶
Compute the embedding vectors for data X
Parameters : X : array-like of shape [n_samples, n_features]
training set.
Returns : self : returns an instance of self.
- fit_transform(X, y=None)¶
Compute the embedding vectors for data X and transform X.
Parameters : X : array-like of shape [n_samples, n_features]
training set.
Returns : X_new: array-like, shape (n_samples, out_dim) :
- set_params(**params)¶
Set the parameters of the estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Returns : self :
- transform(X)¶
Transform new points into embedding space.
Parameters : X : array-like, shape = [n_samples, n_features] Returns : X_new : array, shape = [n_samples, out_dim] Notes
Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs)