manifold.Isomap()

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=1) [source]

Isomap Embedding

Non-linear dimensionality reduction through Isometric Mapping

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, 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.
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

[R185]

Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500)

Methods

`fit`(X[, y])	Compute the embedding vectors for data X
`fit_transform`(X[, y])	Fit the model from data in X and transform X.
`get_params`([deep])	Get parameters for this estimator.
`reconstruction_error`()	Compute the reconstruction error for the embedding.
`set_params`(\\params)	Set the parameters of this estimator.
`transform`(X)	Transform X.

__init__(n_neighbors=5, n_components=2, eigen_solver='auto', tol=0, max_iter=None, path_method='auto', neighbors_algorithm='auto', n_jobs=1) [source]

fit(X, y=None) [source]

Compute the embedding vectors for data X

Parameters:

Parameters:	X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors} Sample data, shape = (n_samples, n_features), in the form of a numpy array, precomputed tree, or NearestNeighbors object.
Returns:	self : returns an instance of self.

X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}

Sample data, shape = (n_samples, n_features), in the form of a numpy array, precomputed tree, or NearestNeighbors object.

Returns:

self : returns an instance of self.

fit_transform(X, y=None) [source]

Fit the model from data in X and transform X.

Parameters:

Parameters:	X: {array-like, sparse matrix, BallTree, KDTree} : Training vector, where n_samples in the number of samples and n_features is the number of features.
Returns:	X_new: array-like, shape (n_samples, n_components) :

X: {array-like, sparse matrix, BallTree, KDTree} :

Training vector, where n_samples in the number of samples and n_features is the number of features.

Returns:

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

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping of string to any Parameter names mapped to their values.

deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params : mapping of string to any

Parameter names mapped to their values.

reconstruction_error() [source]

Compute the reconstruction error for the embedding.

Returns:	reconstruction_error : float

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.

Returns:	self :

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.