sklearn.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')[source]¶ Isomap Embedding
Nonlinear 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’ : FloydWarshall 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.
Attributes: embedding_ : arraylike, shape (n_samples, n_components)
Stores the embedding vectors.
kernel_pca_ : object
KernelPCA object used to implement the embedding.
training_data_ : arraylike, 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_ : arraylike, shape (n_samples, n_samples)
Stores the geodesic distance matrix of training data.
References
[R33] 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')[source]¶

fit
(X, y=None)[source]¶ Compute the embedding vectors for data X
Parameters: X : {arraylike, 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: X: {arraylike, 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: arraylike, shape (n_samples, n_components) :

get_params
(deep=True)[source]¶ Get parameters for this estimator.
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.

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 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)[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.
Parameters: X: arraylike, shape (n_samples, n_features) : Returns: X_new: arraylike, shape (n_samples, n_components) :
