Class KernelCenterer

sklearn/preprocessing/_data.py:2437–2602

r"""Center an arbitrary kernel matrix :math:`K`. Let define a kernel :math:`K` such that: .. math:: K(X, Y) = \phi(X) . \phi(Y)^{T} :math:`\phi(X)` is a function mapping of rows of :math:`X` to a Hilbert space and :math:`K` is of shape `(n_samples, n_samples)`. This c

class KernelCenterer(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
    r"""Center an arbitrary kernel matrix :math:`K`.

    Let define a kernel :math:`K` such that:

    .. math::
        K(X, Y) = \phi(X) . \phi(Y)^{T}

    :math:`\phi(X)` is a function mapping of rows of :math:`X` to a
    Hilbert space and :math:`K` is of shape `(n_samples, n_samples)`.

    This class allows to compute :math:`\tilde{K}(X, Y)` such that:

    .. math::
        \tilde{K(X, Y)} = \tilde{\phi}(X) . \tilde{\phi}(Y)^{T}

    :math:`\tilde{\phi}(X)` is the centered mapped data in the Hilbert
    space.

    `KernelCenterer` centers the features without explicitly computing the
    mapping :math:`\phi(\cdot)`. Working with centered kernels is sometime
    expected when dealing with algebra computation such as eigendecomposition
    for :class:`~sklearn.decomposition.KernelPCA` for instance.

    Read more in the :ref:`User Guide <kernel_centering>`.

    Attributes
    ----------
    K_fit_rows_ : ndarray of shape (n_samples,)
        Average of each column of kernel matrix.

    K_fit_all_ : float
        Average of kernel matrix.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    See Also
    --------
    sklearn.kernel_approximation.Nystroem : Approximate a kernel map
        using a subset of the training data.

    References
    ----------
    .. [1] `Schölkopf, Bernhard, Alexander Smola, and Klaus-Robert Müller.
       "Nonlinear component analysis as a kernel eigenvalue problem."
       Neural computation 10.5 (1998): 1299-1319.
       <https://www.mlpack.org/papers/kpca.pdf>`_

    Examples