pykernels/pykernels/base.py at master · gmum/pykernels · GitHub

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"""
Base classes and methods used by all kernels
"""

__author__ = 'lejlot'

import numpy as np
from abc import abstractmethod, ABCMeta

class Kernel(object):
    """
    Base, abstract kernel class
    """
    __metaclass__ = ABCMeta

    def __call__(self, data_1, data_2):
        return self._compute(data_1, data_2)

    @abstractmethod
    def _compute(self, data_1, data_2):
        """
        Main method which given two lists data_1 and data_2, with
        N and M elements respectively should return a kernel matrix
        of size N x M where K_{ij} = K(data_1_i, data_2_j)
        """
        raise NotImplementedError('This is an abstract class')

    def gram(self, data):
        """
        Returns a Gramian, kernel matrix of matrix and itself
        """
        return self._compute(data, data)

    @abstractmethod
    def dim(self):
        """
        Returns dimension of the feature space
        """
        raise NotImplementedError('This is an abstract class')

    def __str__(self):
        return self.__class__.__name__

    def __repr__(self):
        return str(self)

    def __add__(self, kernel):
        return KernelSum(self, kernel)

    def __mul__(self, value):
        if isinstance(value, Kernel):
            return KernelProduct(self, value)
        else:
            if isinstance(self, ScaledKernel):
                return ScaledKernel(self._kernel, self._scale * value)
            else:
                return ScaledKernel(self, value)

    def __rmul__(self, value):
        return self.__mul__(value)

    def __div__(self, scale):
        return ScaledKernel(self, 1./scale)

    def __pow__(self, value):
        return KernelPower(self, value)

class KernelSum(Kernel):
    """
    Represents sum of a pair of kernels
    """

    def __init__(self, kernel_1, kernel_2):
        self._kernel_1 = kernel_1
        self._kernel_2 = kernel_2

    def _compute(self, data_1, data_2):
        return self._kernel_1._compute(data_1, data_2) + \
               self._kernel_2._compute(data_1, data_2)

    def dim(self):
        # It is too complex to analyze combined dimensionality, so we give a lower bound
        return max(self._kernel_1.dim(), self._kernel_2.dim())

    def __str__(self):
        return '(' + str(self._kernel_1) + ' + ' + str(self._kernel_2) + ')'


class KernelProduct(Kernel):
    """
    Represents product of a pair of kernels
    """

    def __init__(self, kernel_1, kernel_2):
        self._kernel_1 = kernel_1
        self._kernel_2 = kernel_2

    def _compute(self, data_1, data_2):
        return self._kernel_1._compute(data_1, data_2) * \
               self._kernel_2._compute(data_1, data_2)

    def dim(self):
        # It is too complex to analyze combined dimensionality, so we give a lower bound
        return max(self._kernel_1.dim(), self._kernel_2.dim())

    def __str__(self):
        return '(' + str(self._kernel_1) + ' * ' + str(self._kernel_2) + ')'


class KernelPower(Kernel):
    """
    Represents natural power of a kernel
    """

    def __init__(self, kernel, d):
        self._kernel = kernel
        self._d = d
        if not isinstance(d, int) or d<0:
            raise Exception('Kernel power is only defined for non-negative integer degrees')

    def _compute(self, data_1, data_2):
        return self._kernel._compute(data_1, data_2) ** self._d

    def dim(self):
        # It is too complex to analyze combined dimensionality, so we give a lower bound
        return self._kernel.dim()

    def __str__(self):
        return str(self._kernel) + '^' + str(self._d)


class ScaledKernel(Kernel):
    """
    Represents kernel scaled by a float
    """

    def __init__(self, kernel, scale):
        self._kernel = kernel
        self._scale = scale
        if scale < 0:
            raise Exception('Negation of the kernel is not a kernel!')

    def _compute(self, data_1, data_2):
        return self._scale * self._kernel._compute(data_1, data_2)

    def dim(self):
        return self._kernel.dim()

    def __str__(self):
        if self._scale == 1.0:
            return str(self._kernel)
        else:
            return str(self._scale) + ' ' + str(self._kernel)


class GraphKernel(Kernel):
    """
    Base, abstract GraphKernel kernel class
    """
    pass