Method __init__

numpy_ml/utils/kernels.py:185–215

Radial basis function (RBF) / squared exponential kernel. Notes ----- For input vectors :math:`\mathbf{x}` and :math:`\mathbf{y}`, the radial basis function kernel is: .. math:: k(\mathbf{x}, \mathbf{y}) = \exp \left\{ -0.5

(self, sigma=None)

class RBFKernel(KernelBase):
    def __init__(self, sigma=None):
        """
        Radial basis function (RBF) / squared exponential kernel.

        Notes
        -----
        For input vectors :math:`\mathbf{x}` and :math:`\mathbf{y}`, the radial
        basis function kernel is:

        .. math::

            k(\mathbf{x}, \mathbf{y}) = \exp \left\{ -0.5
                \left\lVert \\frac{\mathbf{x} -
                    \mathbf{y}}{\sigma} \\right\\rVert_2^2 \\right\}

        The RBF kernel decreases with distance and ranges between zero (in the
        limit) to one (when **x** = **y**). Notably, the implied feature space
        of the kernel has an infinite number of dimensions.

        Parameters
        ----------
        sigma : float or array of shape `(C,)` or None
            A scaling parameter for the vectors **x** and **y**, producing an
            isotropic kernel if a float, or an anistropic kernel if an array of
            length `C`.  Larger values result in higher resolution / greater
            smoothing. If None, defaults to :math:`\sqrt(C / 2)`. Sometimes
            referred to as the kernel 'bandwidth'. Default is None.
        """
        super().__init__()
        self.hyperparameters = {"id": "RBFKernel"}
        self.parameters = {"sigma": sigma}

    def _kernel(self, X, Y=None):
        """