# LocallyLinearEmbedding¶

class ibex.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=1)

Bases: sklearn.manifold.locally_linear.LocallyLinearEmbedding, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Locally Linear Embedding

Read more in the User Guide.

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’)
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, optional (default = 1)
The number of parallel jobs to run. If -1, then the number of jobs is set to the number of CPU cores.
embedding_vectors_ : array-like, shape [n_components, 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.
 [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)
fit(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Compute the embedding vectors for data X

X : array-like of shape [n_samples, n_features]
training set.

y: Ignored.

self : returns an instance of self.

fit_transform(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Compute the embedding vectors for data X and transform X.

X : array-like of shape [n_samples, n_features]
training set.

y: Ignored.

X_new : array-like, shape (n_samples, n_components)

transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Transform new points into embedding space.

X : array-like, shape = [n_samples, n_features]

X_new : array, shape = [n_samples, n_components]

Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs)