Kernel.Kernel Class Reference

Inheritance diagram for Kernel.Kernel:

Public Member Functions
	__init__ (self, kernel_name='rbf', param=1.0)

Static Public Member Functions
	rbf (x, y, alpha=1.0)
	laplacian (x, y, alpha=1.0)
	sigmoid (x, y, alpha=1.0)
	exponential (x, y, alpha=1.0)
	cosine (x, y, alpha=None)
	morlet_wavelet (x, y, alpha=1.0)
	mexican_hat_wavelet (x, y, alpha=1.0)
	haar_wavelet (x, y, alpha=1.0)
	rational_quadratic (x, y, alpha=1.0)

Public Attributes
	kernel_name
	kernel_param
	ev

Constructor & Destructor Documentation

__init__()

Kernel.Kernel.__init__	(		self,
			kernel_name = 'rbf',
			param = 1.0 )

    Initialize a kernel function object.

    Parameters:
    -----------
    - kernel_name (str): Name of the kernel function. Default is 'rbf'.
    - param (float): Parameter value for the kernel function. Default is 1.0.

Reimplemented in Kernel.CombinedSumKernel, and Kernel.CombinedProductKernel.

Member Function Documentation

cosine()

Kernel.Kernel.cosine ( x, y, alpha = None )

static

    Cosine similarity kernel.

    Computes the cosine similarity between two vectors.

    .. math::
        K(x, y) = \\frac{{\\langle x, y \\rangle}}{{||x|| \\cdot ||y||}}

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (None): This parameter is not used. It's included for compatibility with other kernel functions.

    Returns:
    -----------
    tf.Tensor: Kernel values representing cosine similarity between x and y.

exponential()

Kernel.Kernel.exponential ( x, y, alpha = 1.0 )

static

    Exponential kernel.

    .. math::
        K(x, y) = \\exp\\left(-\\alpha \\sqrt{||x - y||^2}\\right)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the exponential kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

haar_wavelet()

Kernel.Kernel.haar_wavelet ( x, y, alpha = 1.0 )

static

    Haar wavelet kernel.

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the Haar wavelet kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

laplacian()

Kernel.Kernel.laplacian ( x, y, alpha = 1.0 )

static

    Laplacian kernel.

    .. math::
        K(x, y) = \\exp\\left(-\\frac{{||x - y||_1}}{{\\alpha}}\\right)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the Laplacian kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

mexican_hat_wavelet()

Kernel.Kernel.mexican_hat_wavelet ( x, y, alpha = 1.0 )

static

    Mexican hat wavelet kernel.

    .. math::
        K(x, y) = \\left(1 - \\left(\\frac{||x - y||^2}{\\alpha}\\right)^2\\right)
                    \\exp\\left(-\\frac{||x - y||^2}{2\\alpha^2}\\right)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the Mexican hat wavelet kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

morlet_wavelet()

Kernel.Kernel.morlet_wavelet ( x, y, alpha = 1.0 )

static

    Morlet wavelet kernel.

    .. math::
        K(x, y) = \\cos\\left(2\\pi\\frac{||x - y||^2}{\\alpha}\\right)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the Morlet wavelet kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

rational_quadratic()

Kernel.Kernel.rational_quadratic ( x, y, alpha = 1.0 )

static

    Rational quadratic kernel.

    .. math::
        K(x, y) = 1 - \\frac{||x - y||^2}{||x - y||^2 + \\alpha}

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the rational quadratic kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

rbf()

Kernel.Kernel.rbf ( x, y, alpha = 1.0 )

static

    Radial Basis Function (RBF) kernel.

    .. math::
        K(x, y) = \\exp\\left(-\\frac{{||x - y||^2}}{{2 \\alpha^2}}\\right)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the RBF kernel. Default is 1.0.

    Returns:
    tf.Tensor: Kernel values.

sigmoid()

Kernel.Kernel.sigmoid ( x, y, alpha = 1.0 )

static

    Sigmoid kernel.

    .. math::
        K(x, y) = \\tanh(\\alpha \\cdot \\langle x, y \\rangle)

    Parameters:
    -----------
    - x (tf.Tensor): Input tensor.
    - y (tf.Tensor): Input tensor.
    - alpha (float): Parameter value for the sigmoid kernel. Default is 1.0.

    Returns:
    -----------
    tf.Tensor: Kernel values.

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The documentation for this class was generated from the following file:

• Resources/Kernel.py