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)[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 or None :
Number of components. If None, all non-zero components are kept.
kernel: “linear” | “poly” | “rbf” | “sigmoid” | “cosine” | “precomputed” :
Kernel. Default: “linear”
degree : int, default=3
Degree for poly kernels. Ignored by other kernels.
gamma : float, optional
Kernel coefficient for rbf and poly kernels. Default: 1/n_features. Ignored by other kernels.
coef0 : float, optional
Independent term in poly and sigmoid kernels. Ignored by other kernels.
kernel_params : mapping of string to any, optional
Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
alpha: int :
Hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True). Default: 1.0
fit_inverse_transform: bool :
Learn the inverse transform for non-precomputed kernels. (i.e. learn to find the pre-image of a point) Default: False
eigen_solver: string [‘auto’|’dense’|’arpack’] :
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 :
convergence tolerance for arpack. Default: 0 (optimal value will be chosen by arpack)
max_iter : int
maximum number of iterations for arpack Default: None (optimal value will be chosen by arpack)
remove_zero_eig : boolean, default=True
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.
Attributes: lambdas_ : :
Eigenvalues of the centered kernel matrix
alphas_ : :
Eigenvectors of the centered kernel matrix
dual_coef_ : :
Inverse transform matrix
X_transformed_fit_ : :
Projection of the fitted data on the kernel principal components
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)[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 former have parameters of the form
<component>__<parameter>so that it’s possible to update each component of a nested object.Returns: self :
