`sklearn.manifold`.Isomap¶

class sklearn.manifold.Isomap(*, n_neighbors=5, radius=None, 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.

Non-linear dimensionality reduction through Isometric Mapping

See also

sklearn.decomposition.PCA: Principal component analysis that is a linear dimensionality reduction method.
sklearn.decomposition.KernelPCA: Non-linear dimensionality reduction using kernels and PCA.
MDS: Manifold learning using multidimensional scaling.
TSNE: T-distributed Stochastic Neighbor Embedding.
LocallyLinearEmbedding: Manifold learning using Locally Linear Embedding.
SpectralEmbedding: Spectral embedding for non-linear dimensionality.

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_feature_names_out`([input_features])	Get output feature names for transformation.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`reconstruction_error`()	Compute the reconstruction error for the embedding.
`set_output`(*[, transform])	Set output container.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(X)	Transform X.

fit(X, y=None)[source]¶

Compute the embedding vectors for data X.

Parameters:

X{array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}: Sample data, shape = (n_samples, n_features), in the form of a numpy array, sparse matrix, precomputed tree, or NearestNeighbors object.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: Returns a fitted instance of self.

fit_transform(X, y=None)[source]¶

Fit the model from data in X and transform X.

Parameters:

X{array-like, sparse matrix, BallTree, KDTree}: Training vector, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.

Returns:

X_newarray-like, shape (n_samples, n_components): X transformed in the new space.

get_feature_names_out(input_features=None)[source]¶

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

Parameters:

input_featuresarray-like of str or None, default=None: Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects: Transformed feature names.

get_metadata_routing()[source]¶

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

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:

paramsdict: Parameter names mapped to their values.

reconstruction_error()[source]¶

Compute the reconstruction error for the embedding.

Returns:

reconstruction_errorfloat: Reconstruction error.

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_output(*, transform=None)[source]¶

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:

transform{“default”, “pandas”}, default=None

Configure output of transform and fit_transform.

"default": Default output format of a transformer
"pandas": DataFrame output
None: Transform configuration is unchanged

Returns:

selfestimator instance: Estimator instance.

set_params(**params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). 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:

selfestimator instance: 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:

X{array-like, sparse matrix}, 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_newarray-like, shape (n_queries, n_components): X transformed in the new space.

Examples using `sklearn.manifold.Isomap`¶

Release Highlights for scikit-learn 0.22

Comparison of Manifold Learning methods

Manifold Learning methods on a severed sphere

Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…

Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...

sklearn.manifold.Isomap¶

Examples using sklearn.manifold.Isomap¶

`sklearn.manifold`.Isomap¶

Examples using `sklearn.manifold.Isomap`¶