sklearn.manifold.Isomap
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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)
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Isomap Embedding
Non-linear dimensionality reduction through Isometric Mapping
Read more in the User Guide.
- Parameters
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n_neighborsint, default=5
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number of neighbors to consider for each point.
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n_componentsint, default=2
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number of coordinates for the manifold
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eigen_solver{‘auto’, ‘arpack’, ‘dense’}, default=’auto’
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‘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.
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tolfloat, default=0
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Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == ‘dense’.
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max_iterint, default=None
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Maximum number of iterations for the arpack solver. not used if eigen_solver == ‘dense’.
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path_method{‘auto’, ‘FW’, ‘D’}, default=’auto’
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Method to use in finding shortest path.
‘auto’ : attempt to choose the best algorithm automatically.
‘FW’ : Floyd-Warshall algorithm.
‘D’ : Dijkstra’s algorithm.
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neighbors_algorithm{‘auto’, ‘brute’, ‘kd_tree’, ‘ball_tree’}, default=’auto’
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Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance.
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n_jobsint or None, default=None
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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”
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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.
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pint, default=2
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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.
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metric_paramsdict, default=None
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Additional keyword arguments for the metric function.
New in version 0.22.
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- Attributes
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embedding_array-like, shape (n_samples, n_components)
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Stores the embedding vectors.
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kernel_pca_object
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KernelPCA
object used to implement the embedding. -
nbrs_sklearn.neighbors.NearestNeighbors instance
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Stores nearest neighbors instance, including BallTree or KDtree if applicable.
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dist_matrix_array-like, shape (n_samples, n_samples)
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Stores the geodesic distance matrix of training data.
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References
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1
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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.
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fit(X, y=None)
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Compute the embedding vectors for data X
- Parameters
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X{array-like, sparse graph, BallTree, KDTree, NearestNeighbors}
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Sample data, shape = (n_samples, n_features), in the form of a numpy array, sparse graph, precomputed tree, or NearestNeighbors object.
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yIgnored
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- Returns
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selfreturns an instance of self.
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fit_transform(X, y=None)
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Fit the model from data in X and transform X.
- Parameters
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X{array-like, sparse graph, BallTree, KDTree}
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Training vector, where n_samples in the number of samples and n_features is the number of features.
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yIgnored
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- Returns
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X_newarray-like, shape (n_samples, n_components)
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get_params(deep=True)
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Get parameters for this estimator.
- Parameters
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deepbool, default=True
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If True, will return the parameters for this estimator and contained subobjects that are estimators.
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- Returns
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paramsdict
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Parameter names mapped to their values.
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reconstruction_error()
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Compute the reconstruction error for the embedding.
- Returns
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reconstruction_errorfloat
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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)
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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
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**paramsdict
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Estimator parameters.
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- Returns
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selfestimator instance
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Estimator instance.
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transform(X)
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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
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Xarray-like, shape (n_queries, n_features)
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If neighbors_algorithm=’precomputed’, X is assumed to be a distance matrix or a sparse graph of shape (n_queries, n_samples_fit).
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- Returns
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X_newarray-like, shape (n_queries, n_components)
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Examples using sklearn.manifold.Isomap
© 2007–2020 The scikit-learn developers
Licensed under the 3-clause BSD License.
https://scikit-learn.org/0.24/modules/generated/sklearn.manifold.Isomap.html