sklearn.manifold.Isomap — scikit-learn 0.20.4 documentation (original) (raw)

class sklearn.manifold. Isomap(n_neighbors=5, n_components=2, eigen_solver='auto', tol=0, max_iter=None, path_method='auto', neighbors_algorithm='auto', n_jobs=None)[source]¶

Isomap Embedding

Non-linear dimensionality reduction through Isometric Mapping

Read more in the User Guide.

| Parameters: | n_neighbors : integer number of neighbors to consider for each point. n_components : integer number of coordinates for the manifold eigen_solver : [‘auto’|’arpack’|’dense’] ‘auto’ : Attempt to choose the most efficient solver for the given problem. ‘arpack’ : Use Arnoldi decomposition to find the eigenvalues and eigenvectors. ‘dense’ : Use a direct solver (i.e. LAPACK) for the eigenvalue decomposition. tol : float Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == ‘dense’. max_iter : integer Maximum number of iterations for the arpack solver. not used if eigen_solver == ‘dense’. path_method : string [‘auto’|’FW’|’D’] Method to use in finding shortest path. ‘auto’ : attempt to choose the best algorithm automatically. ‘FW’ : Floyd-Warshall algorithm. ‘D’ : Dijkstra’s algorithm. neighbors_algorithm : string [‘auto’|’brute’|’kd_tree’|’ball_tree’] Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance. 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 Glossaryfor more details. | | ----------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Attributes: | embedding_ : array-like, shape (n_samples, n_components) Stores the embedding vectors. kernel_pca_ : object KernelPCA object used to implement the embedding. training_data_ : array-like, shape (n_samples, n_features) Stores the training data. nbrs_ : sklearn.neighbors.NearestNeighbors instance Stores nearest neighbors instance, including BallTree or KDtree if applicable. dist_matrix_ : array-like, shape (n_samples, n_samples) Stores the geodesic distance matrix of training data. |

References

Examples

from sklearn.datasets import load_digits from sklearn.manifold import Isomap X, _ = load_digits(return_X_y=True) X.shape (1797, 64) embedding = Isomap(n_components=2) X_transformed = embedding.fit_transform(X[:100]) X_transformed.shape (100, 2)

Methods

__init__(n_neighbors=5, n_components=2, eigen_solver='auto', tol=0, max_iter=None, path_method='auto', neighbors_algorithm='auto', n_jobs=None)[source]¶

fit(X, y=None)[source]¶

Compute the embedding vectors for data X

fit_transform(X, y=None)[source]¶

Fit the model from data in X and transform X.

get_params(deep=True)[source]¶

Get parameters for this estimator.

reconstruction_error()[source]¶

Compute the reconstruction error for the embedding.

Notes

The cost function of an isomap embedding is

E = frobenius_norm[K(D) - K(D_fit)] / n_samples

Where D is the matrix of distances for the input data X, D_fit is the matrix of distances for the output embedding X_fit, and K is the isomap kernel:

K(D) = -0.5 * (I - 1/n_samples) * D^2 * (I - 1/n_samples)

set_params(**params)[source]¶

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.

transform(X)[source]¶

Transform X.

This is implemented by linking the points X into the graph of geodesic distances of the training data. First the n_neighbors nearest neighbors of X are found in the training data, and from these the shortest geodesic distances from each point in X to each point in the training data are computed in order to construct the kernel. The embedding of X is the projection of this kernel onto the embedding vectors of the training set.

Examples using sklearn.manifold.Isomap¶