.. _`Kernel Principal Component Analysis (KPCA)`:

.. _`org.sysess.sympathy.machinelearning.kpca`:

Kernel Principal Component Analysis (KPCA)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. image:: PCA.svg
   :width: 48


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. Default="linear".


  - *degree*

    Degree for poly kernels. Ignored by other kernels.


  - *gamma*

    Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other
    kernels.


  - *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).


  - *fit_inverse_transform*

    Learn the inverse transform for non-precomputed kernels.
    (i.e. learn to find the pre-image of a point)


  - *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, arpack may be more efficient
    than the dense eigensolver.


  - *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*

    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'.

    .. versionadded:: 0.18


  - *n_jobs*

    The number of parallel jobs to run.
    If `-1`, then the number of jobs is set to the number of CPU cores.

    .. versionadded:: 0.18




:Attributes:


  - *lambdas_*

    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_*

    Eigenvectors of the centered kernel matrix. If `n_components` and
    `remove_zero_eig` are not set, then all components are stored.


  - *dual_coef_*

    Inverse transform matrix. Set if `fit_inverse_transform` is True.


  - *X_transformed_fit_*

    Projection of the fitted data on the kernel principal components.


  - *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.




:Inputs:


:Outputs:
    **model** : model
        Model

*Ports*:

    **Outputs**:

        :model: model

            Model

*Configuration*:

    **n_components**
        Number of components. If None, all non-zero components are kept.
    **kernel**
        Kernel. Default="linear".
    **degree**
        Degree for poly kernels. Ignored by other kernels.
    **gamma**
        Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other
        kernels.
    **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).
    **fit_inverse_transform**
        Learn the inverse transform for non-precomputed kernels.
        (i.e. learn to find the pre-image of a point)
    **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, arpack may be more efficient
        than the dense eigensolver.
    **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**
        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'.

        .. versionadded:: 0.18
    **n_jobs**
        The number of parallel jobs to run.
        If `-1`, then the number of jobs is set to the number of CPU cores.

        .. versionadded:: 0.18

.. automodule:: node_decomposition

.. class:: KernelPCA