sklearn.decomposition.KernelPCA¶
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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=1)[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_components : int, default=None
Number of components. If None, all non-zero components are kept.
kernel : “linear” | “poly” | “rbf” | “sigmoid” | “cosine” | “precomputed”
Kernel. Default=”linear”.
gamma : float, default=1/n_features
Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels.
degree : int, default=3
Degree for poly kernels. Ignored by other kernels.
coef0 : float, default=1
Independent term in poly and sigmoid kernels. Ignored by other kernels.
kernel_params : mapping of string to any, default=None
Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
alpha : int, default=1.0
Hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True).
fit_inverse_transform : bool, default=False
Learn the inverse transform for non-precomputed kernels. (i.e. learn to find the pre-image of a point)
eigen_solver : string [‘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.
tol : float, default=0
Convergence tolerance for arpack. If 0, optimal value will be chosen by arpack.
max_iter : int, default=None
Maximum number of iterations for arpack. If None, optimal value will be chosen by arpack.
remove_zero_eig : boolean, 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_state : int, 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_X : boolean, 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_jobs : int, default=1
The number of parallel jobs to run. If -1, then the number of jobs is set to the number of CPU cores.
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. Set if fit_inverse_transform is True.
X_transformed_fit_ : array, (n_samples, n_components)
Projection of the fitted data on the kernel principal components.
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.
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. -
__init__(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=1)[source]¶
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fit(X, y=None)[source]¶ Fit the model from data in X.
Parameters: X : array-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: self : object
Returns the instance itself.
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fit_transform(X, y=None, **params)[source]¶ Fit the model from data in X and transform X.
Parameters: X : array-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_new : array-like, shape (n_samples, n_components)
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get_params(deep=True)[source]¶ Get parameters for this estimator.
Parameters: deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params : mapping of string to any
Parameter names mapped to their values.
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inverse_transform(X)[source]¶ Transform X back to original space.
Parameters: X : array-like, shape (n_samples, n_components) Returns: X_new : array-like, shape (n_samples, n_features) References
“Learning to Find Pre-Images”, G BakIr et al, 2004.
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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 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 :
