`sklearn.decomposition`.KernelPCA¶

class sklearn.decomposition.KernelPCA(n_components=None, *, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, alpha=1.0, fit_inverse_transform=False, eigen_solver='auto', tol=0, max_iter=None, iterated_power='auto', remove_zero_eig=False, random_state=None, copy_X=True, n_jobs=None)[source]¶

Kernel Principal component analysis (KPCA).

Non-linear dimensionality reduction through the use of kernels (see Pairwise metrics, Affinities and Kernels).

It uses the scipy.linalg.eigh LAPACK implementation of the full SVD or the scipy.sparse.linalg.eigsh ARPACK implementation of the truncated SVD, depending on the shape of the input data and the number of components to extract. It can also use a randomized truncated SVD by the method proposed in [3], see eigen_solver.

See also

FastICA: A fast algorithm for Independent Component Analysis.
IncrementalPCA: Incremental Principal Component Analysis.
NMF: Non-Negative Matrix Factorization.
PCA: Principal Component Analysis.
SparsePCA: Sparse Principal Component Analysis.
TruncatedSVD: Dimensionality reduction using truncated SVD.

References

1: Schölkopf, Bernhard, Alexander Smola, and Klaus-Robert Müller. “Kernel principal component analysis.” International conference on artificial neural networks. Springer, Berlin, Heidelberg, 1997.
2: Bakır, Gökhan H., Jason Weston, and Bernhard Schölkopf. “Learning to find pre-images.” Advances in neural information processing systems 16 (2004): 449-456.
3(1,2,3): Halko, Nathan, Per-Gunnar Martinsson, and Joel A. Tropp. “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions.” SIAM review 53.2 (2011): 217-288.
4: Martinsson, Per-Gunnar, Vladimir Rokhlin, and Mark Tygert. “A randomized algorithm for the decomposition of matrices.” Applied and Computational Harmonic Analysis 30.1 (2011): 47-68.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import KernelPCA
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = KernelPCA(n_components=7, kernel='linear')
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

Methods

`fit`(X[, y])	Fit the model from data in X.
`fit_transform`(X[, y])	Fit the model from data in X and transform X.
`get_params`([deep])	Get parameters for this estimator.
`inverse_transform`(X)	Transform X back to original space.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(X)	Transform X.

property alphas_¶: DEPRECATED: Attribute alphas_ was deprecated in version 1.0 and will be removed in 1.2. Use eigenvectors_ instead.

fit(X, y=None)[source]¶

Fit the model from data in X.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): 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

selfobject: Returns the instance itself.

fit_transform(X, y=None, **params)[source]¶

Fit the model from data in X and transform X.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): 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.
**paramskwargs: Parameters (keyword arguments) and values passed to the fit_transform instance.

Returns

X_newndarray of shape (n_samples, n_components): Returns the instance itself.

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.

inverse_transform(X)[source]¶

Transform X back to original space.

inverse_transform approximates the inverse transformation using a learned pre-image. The pre-image is learned by kernel ridge regression of the original data on their low-dimensional representation vectors.

Note

When users want to compute inverse transformation for ‘linear’ kernel, it is recommended that they use PCA instead. Unlike PCA, KernelPCA’s inverse_transform does not reconstruct the mean of data when ‘linear’ kernel is used due to the use of centered kernel.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_components): Training vector, where n_samples is the number of samples and n_features is the number of features.

Returns

X_newndarray of shape (n_samples, n_features): Returns the instance itself.

References

Bakır, Gökhan H., Jason Weston, and Bernhard Schölkopf. “Learning to find pre-images.” Advances in neural information processing systems 16 (2004): 449-456.

property lambdas_¶: DEPRECATED: Attribute lambdas_ was deprecated in version 1.0 and will be removed in 1.2. Use eigenvalues_ instead.

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.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features): Training vector, where n_samples is the number of samples and n_features is the number of features.

Returns

X_newndarray of shape (n_samples, n_components): Returns the instance itself.

Examples using `sklearn.decomposition.KernelPCA`¶

sklearn.decomposition.KernelPCA¶

Examples using sklearn.decomposition.KernelPCA¶

`sklearn.decomposition`.KernelPCA¶

Examples using `sklearn.decomposition.KernelPCA`¶