graphkit-learn/pygraph/utils/kernels.py

"""Those who are not graph kernels. We can be kernels for nodes or edges!
These kernels are defined between pairs of vectors.
"""
import numpy as np

def deltakernel(x, y):
    """Delta kernel. Return 1 if x == y, 0 otherwise.

    Parameters
    ----------
    x, y : any
        Two parts to compare.

    Return
    ------
    kernel : integer
        Delta kernel.

    References
    ----------
    [1] H. Kashima, K. Tsuda, and A. Inokuchi. Marginalized kernels between 
    labeled graphs. In Proceedings of the 20th International Conference on 
    Machine Learning, Washington, DC, United States, 2003.
    """
    return x == y  #(1 if condition else 0)


def gaussiankernel(x, y, gamma=None):
    """Gaussian kernel.
    Compute the rbf (gaussian) kernel between x and y:

        K(x, y) = exp(-gamma ||x-y||^2).

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

    Parameters
    ----------
    x, y : array

    gamma : float, default None
        If None, defaults to 1.0 / n_features

    Returns
    -------
    kernel : float
    """
    if gamma is None:
        gamma = 1.0 / len(x)

    xt = np.array([float(itm) for itm in x])
    yt = np.array([float(itm) for itm in y])
    kernel = xt - yt
    kernel = kernel ** 2
    kernel = np.sum(kernel)
    kernel *= -gamma
    kernel = np.exp(kernel)
    return kernel


def polynomialkernel(x, y, d=1, c=0):
    """Polynomial kernel.
    Compute the polynomial kernel between x and y:

        K(x, y) = <x, y> ^d + c.

    Parameters
    ----------
    x, y : array

    d : integer, default 1
    
    c : float, default 0

    Returns
    -------
    kernel : float
    """
    return np.dot(x, y) ** d + c


def linearkernel(x, y):
    """Polynomial kernel.
    Compute the polynomial kernel between x and y:

        K(x, y) = <x, y>.

    Parameters
    ----------
    x, y : array

    d : integer, default 1
    
    c : float, default 0

    Returns
    -------
    kernel : float
    """
    return np.dot(x, y)


def kernelsum(k1, k2, d11, d12, d21=None, d22=None, lamda1=1, lamda2=1):
    """Sum of a pair of kernels.

    k = lamda1 * k1(d11, d12) + lamda2 * k2(d21, d22)

    Parameters
    ----------
    k1, k2 : function
        A pair of kernel functions.
    d11, d12:
        Inputs of k1. If d21 or d22 is None, apply d11, d12 to both k1 and k2.
    d21, d22:
        Inputs of k2.
    lamda1, lamda2: float
        Coefficients of the product.

    Return
    ------
    kernel : integer

    """
    if d21 == None or d22 == None:
        kernel = lamda1 * k1(d11, d12) + lamda2 * k2(d11, d12)
    else:
        kernel = lamda1 * k1(d11, d12) + lamda2 * k2(d21, d22)
    return kernel


def kernelproduct(k1, k2, d11, d12, d21=None, d22=None, lamda=1):
    """Product of a pair of kernels.

    k = lamda * k1(d11, d12) * k2(d21, d22)

    Parameters
    ----------
    k1, k2 : function
        A pair of kernel functions.
    d11, d12:
        Inputs of k1. If d21 or d22 is None, apply d11, d12 to both k1 and k2.
    d21, d22:
        Inputs of k2.
    lamda: float
        Coefficient of the product.

    Return
    ------
    kernel : integer
    """
    if d21 == None or d22 == None:
        kernel = lamda * k1(d11, d12) * k2(d11, d12)
    else:
        kernel = lamda * k1(d11, d12) * k2(d21, d22)
    return kernel


if __name__ == '__main__':
    o = polynomialkernel([1, 2], [3, 4], 2, 3)