`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, 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).

Read more in the User Guide.

Parameters

n_componentsint, default=None: Number of components. If None, all non-zero components are kept.
kernel{‘linear’, ‘poly’, ‘rbf’, ‘sigmoid’, ‘cosine’, ‘precomputed’}, default=’linear’: Kernel used for PCA.
gammafloat, default=None: Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels. If gamma is None, then it is set to 1/n_features.
degreeint, default=3: Degree for poly kernels. Ignored by other kernels.
coef0float, default=1: Independent term in poly and sigmoid kernels. Ignored by other kernels.
kernel_paramsdict, default=None: Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
alphafloat, default=1.0: Hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True).
fit_inverse_transformbool, default=False: Learn the inverse transform for non-precomputed kernels. (i.e. learn to find the pre-image of a point)
eigen_solver{‘auto’, ‘dense’, ‘arpack’}, default=’auto’: Select eigensolver to use. If n_components is much less than the number of training samples, arpack may be more efficient than the dense eigensolver.
tolfloat, default=0: Convergence tolerance for arpack. If 0, optimal value will be chosen by arpack.
max_iterint, default=None: Maximum number of iterations for arpack. If None, optimal value will be chosen by arpack.
remove_zero_eigbool, default=False: If True, then all components with zero eigenvalues are removed, so that the number of components in the output may be < n_components (and sometimes even zero due to numerical instability). When n_components is None, this parameter is ignored and components with zero eigenvalues are removed regardless.
random_stateint, RandomState instance or None, default=None: Used when eigen_solver == ‘arpack’. Pass an int for reproducible results across multiple function calls. See Glossary.

New in version 0.18.
copy_Xbool, default=True: If True, input X is copied and stored by the model in the X_fit_ attribute. If no further changes will be done to X, setting copy_X=False saves memory by storing a reference.

New in version 0.18.
n_jobsint, default=None: The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

New in version 0.18.

Attributes

lambdas_ndarray of shape (n_components,): Eigenvalues of the centered kernel matrix in decreasing order. If n_components and remove_zero_eig are not set, then all values are stored.
alphas_ndarray of shape (n_samples, n_components): Eigenvectors of the centered kernel matrix. If n_components and remove_zero_eig are not set, then all components are stored.
dual_coef_ndarray of shape (n_samples, n_features): Inverse transform matrix. Only available when fit_inverse_transform is True.
X_transformed_fit_ndarray of shape (n_samples, n_components): Projection of the fitted data on the kernel principal components. Only available when fit_inverse_transform is True.
X_fit_ndarray of shape (n_samples, n_features): The data used to fit the model. If copy_X=False, then X_fit_ is a reference. This attribute is used for the calls to transform.

References

Kernel PCA was introduced in:: Bernhard Schoelkopf, Alexander J. Smola, and Klaus-Robert Mueller. 1999. Kernel principal component analysis. In Advances in kernel methods, MIT Press, Cambridge, MA, USA 327-352.

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.

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 in the number of samples and n_features is the number of features.

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 in the number of samples and n_features is the number of features.

Returns

X_newndarray of 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

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)

Returns

X_newndarray of shape (n_samples, n_features)

References

“Learning to Find Pre-Images”, G BakIr et al, 2004.

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)

Returns

X_newndarray of shape (n_samples, n_components)

sklearn.decomposition.KernelPCA¶

Examples using sklearn.decomposition.KernelPCA¶

`sklearn.decomposition`.KernelPCA¶

Examples using `sklearn.decomposition.KernelPCA`¶