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', n_jobs=None, metric='minkowski', p=2, metric_params=None)[source]¶ Isomap Embedding
Nonlinear dimensionality reduction through Isometric Mapping
Read more in the User Guide.
 Parameters
 n_neighborsinteger
number of neighbors to consider for each point.
 n_componentsinteger
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.
 tolfloat
Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == ‘dense’.
 max_iterinteger
Maximum number of iterations for the arpack solver. not used if eigen_solver == ‘dense’.
 path_methodstring [‘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_algorithmstring [‘auto’’brute’’kd_tree’’ball_tree’]
Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance.
 n_jobsint or None, default=None
The number of parallel jobs to run.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. metricstring, or callable, default=”minkowski”
The metric to use when calculating distance between instances in a feature array. If metric is a string or callable, it must be one of the options allowed by
sklearn.metrics.pairwise_distances
for its metric parameter. If metric is “precomputed”, X is assumed to be a distance matrix and must be square. X may be a Glossary.New in version 0.22.
 pint, default=2
Parameter for the Minkowski metric from sklearn.metrics.pairwise.pairwise_distances. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
New in version 0.22.
 metric_paramsdict, default=None
Additional keyword arguments for the metric function.
New in version 0.22.
 Attributes
 embedding_arraylike, shape (n_samples, n_components)
Stores the embedding vectors.
 kernel_pca_object
KernelPCA
object used to implement the embedding. 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
 1
Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500)
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
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.
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=None, metric='minkowski', p=2, metric_params=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(X, y=None)[source]¶ Compute the embedding vectors for data X
 Parameters
 X{arraylike, sparse graph, BallTree, KDTree, NearestNeighbors}
Sample data, shape = (n_samples, n_features), in the form of a numpy array, sparse graph, precomputed tree, or NearestNeighbors object.
 yIgnored
 Returns
 selfreturns an instance of self.

fit_transform
(X, y=None)[source]¶ Fit the model from data in X and transform X.
 Parameters
 X{arraylike, sparse graph, BallTree, KDTree}
Training vector, where n_samples in the number of samples and n_features is the number of features.
 yIgnored
 Returns
 X_newarraylike, shape (n_samples, n_components)

get_params
(deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsmapping of string to any
Parameter names mapped to their values.

reconstruction_error
()[source]¶ Compute the reconstruction error for the embedding.
 Returns
 reconstruction_errorfloat
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. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.

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
 Xarraylike, shape (n_queries, n_features)
If neighbors_algorithm=’precomputed’, X is assumed to be a distance matrix or a sparse graph of shape (n_queries, n_samples_fit).
 Returns
 X_newarraylike, shape (n_queries, n_components)