Kernel Principal Component Analysis (KPCA)

Non-linear dimensionality reduction through the use of kernels

Documentation

Non-linear dimensionality reduction through the use of kernels

Configuration:

• n_components

  Number of components. If None, all non-zero components are kept.

• kernel

  Kernel used for PCA.

• fit_inverse_transform

  Learn the inverse transform for non-precomputed kernels (i.e. learn to find the pre-image of a point). This method is based on _.

• degree

  Degree for poly kernels. Ignored by other kernels.

• gamma

  Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels. If gamma is None, then it is set to 1/n_features.

• coef0

  Independent term in poly and sigmoid kernels. Ignored by other kernels.

• alpha

  Hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True).

• remove_zero_eig

  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.

• eigen_solver

  Select eigensolver to use. If n_components is much less than the number of training samples, randomized (or arpack to a smaller extend) may be more efficient than the dense eigensolver. Randomized SVD is performed according to the method of Halko et al _.

  auto :

  the solver is selected by a default policy based on n_samples (the number of training samples) and n_components: if the number of components to extract is less than 10 (strict) and the number of samples is more than 200 (strict), the ‘arpack’ method is enabled. Otherwise the exact full eigenvalue decomposition is computed and optionally truncated afterwards (‘dense’ method).

  dense :

  run exact full eigenvalue decomposition calling the standard LAPACK solver via scipy.linalg.eigh, and select the components by postprocessing

  arpack :

  run SVD truncated to n_components calling ARPACK solver using scipy.sparse.linalg.eigsh. It requires strictly 0 < n_components < n_samples

  randomized :

  run randomized SVD by the method of Halko et al. _. The current implementation selects eigenvalues based on their module; therefore using this method can lead to unexpected results if the kernel is not positive semi-definite. See also _.

  Changed in version 1.0: ‘randomized’ was added.

• tol

  Convergence tolerance for arpack. If 0, optimal value will be chosen by arpack.

• max_iter

  Maximum number of iterations for arpack. If None, optimal value will be chosen by arpack.

• random_state

  Used when eigen_solver == ‘arpack’ or ‘randomized’. Pass an int for reproducible results across multiple function calls. See random_state.

  New in version 0.18.

• n_jobs

  The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See n_jobs for more details.

  New in version 0.18.

Attributes:

• lambdas_

  Same as eigenvalues_ but this attribute is deprecated.

  Deprecated since version 1.0: lambdas_ was renamed to eigenvalues_ in version 1.0 and will be removed in 1.2.

• alphas_

  Same as eigenvectors_ but this attribute is deprecated.

  Deprecated since version 1.0: alphas_ was renamed to eigenvectors_ in version 1.0 and will be removed in 1.2.

• dual_coef_

  Inverse transform matrix. Only available when fit_inverse_transform is True.

• X_transformed_fit_

  Projection of the fitted data on the kernel principal components. Only available when fit_inverse_transform is True.

• X_fit_

  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.

Input ports:

Output ports:

modelmodel

Model

Definition

Input ports

Output ports

model

model

Model

class node_decomposition.KernelPCA