`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”: Kernel. Default=”linear”.
gammafloat, default=1/n_features: Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels.
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_paramsmapping of string to any, default=None: Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
alphaint, 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_solverstring [‘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_eigboolean, 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, optional (default=None): If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when eigen_solver == ‘arpack’.

New in version 0.18.
copy_Xboolean, 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 or None, optional (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_array, (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_array, (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_array, (n_samples, n_features): Inverse transform matrix. Only available when fit_inverse_transform is True.
X_transformed_fit_array, (n_samples, n_components): Projection of the fitted data on the kernel principal components. Only available when fit_inverse_transform is True.
X_fit_(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`(self, X[, y])	Fit the model from data in X.
`fit_transform`(self, X[, y])	Fit the model from data in X and transform X.
`get_params`(self[, deep])	Get parameters for this estimator.
`inverse_transform`(self, X)	Transform X back to original space.
`set_params`(self, \\params)	Set the parameters of this estimator.
`transform`(self, X)	Transform X.

__init__(self, 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]¶: Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y=None)[source]¶

Fit the model from data in X.

Parameters

Xarray-like, 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(self, X, y=None, **params)[source]¶

Fit the model from data in X and transform X.

Parameters

Xarray-like, 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_newarray-like, shape (n_samples, n_components)

get_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepboolean, optional: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsmapping of string to any: Parameter names mapped to their values.

inverse_transform(self, X)[source]¶

Transform X back to original space.

Parameters

Xarray-like, shape (n_samples, n_components)

Returns

X_newarray-like, shape (n_samples, n_features)

References

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

set_params(self, **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

transform(self, X)[source]¶

Transform X.

Parameters

Xarray-like, shape (n_samples, n_features)

Returns

X_newarray-like, shape (n_samples, n_components)

sklearn.decomposition.KernelPCA¶

`sklearn.decomposition`.KernelPCA¶