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)
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Isomap Embedding
Non-linear 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’ : 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 |
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Attributes: |
embedding_ : array-like, shape (n_samples, n_components) Stores the embedding vectors. kernel_pca_ : object
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. |
[R185] | Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500) |
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)
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fit(X, y=None)
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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, precomputed tree, or NearestNeighbors object. |
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Returns: |
self : returns an instance of self. |
fit_transform(X, y=None)
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Fit the model from data in X and transform X.
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. |
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Returns: |
X_new: array-like, shape (n_samples, n_components) : |
get_params(deep=True)
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Get parameters for this estimator.
Parameters: |
deep: boolean, optional : If True, will return the parameters for this estimator and contained subobjects that are estimators. |
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Returns: |
params : mapping of string to any Parameter names mapped to their values. |
reconstruction_error()
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Compute the reconstruction error for the embedding.
Returns: | reconstruction_error : float |
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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 : |
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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: | X: array-like, shape (n_samples, n_features) : |
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Returns: | X_new: array-like, shape (n_samples, n_components) : |
sklearn.manifold.Isomap
© 2007–2016 The scikit-learn developers
Licensed under the 3-clause BSD License.
http://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html