com.imsl.datamining.supportvectormachine

Class PolynomialKernel

java.lang.Object

com.imsl.datamining.supportvectormachine.Kernel

com.imsl.datamining.supportvectormachine.PolynomialKernel

All Implemented Interfaces:

Cloneable

public class PolynomialKernel
extends Kernel

Specifies the polynomial kernel for support vector machines.

The kernel function at two data nodes, \(x_i\) and \(x_j\), is given by \(K(x_i , x_j) = (\gamma x_i^Tx_j + r)^d\), where \(\gamma \gt 0\), \(r\), and \(d > 0 \) are configurable parameters.

Constructor Summary

Constructors

Constructor and Description
PolynomialKernel() Constructor for the polynomial kernel.
PolynomialKernel(double gamma, double r, int degree) Constructs a polynomial kernel.
PolynomialKernel(PolynomialKernel polyKernel) Constructs a copy of the input PolynomialKernel kernel.

Method Summary

Modifier and Type	Method and Description
PolynomialKernel	clone() Clones a PolynomialKernel kernel.
double	kernelFunction(DataNode[][] x, int i, int j) Calculates the kernel function between two DataNodes.
double	kernelFunction(DataNode[] x, DataNode[] y) Calculates the kernel function between two DataNodes.
void	setParameters(double... kParams) Sets the parameters for the polynomial kernel.

Methods inherited from class com.imsl.datamining.supportvectormachine.Kernel

dot, getParameters

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PolynomialKernel

public PolynomialKernel()

Constructor for the polynomial kernel.

The default values for the polynomial kernel are \(\gamma\)=1.0, r=0.0, and degree=1.

PolynomialKernel

public PolynomialKernel(PolynomialKernel polyKernel)

Constructs a copy of the input PolynomialKernel kernel.

Parameters:

polyKernel - a PolynomialKernel kernel

PolynomialKernel

public PolynomialKernel(double gamma,
                        double r,
                        int degree)

Constructs a polynomial kernel.

Parameters:

gamma - a double, the polynomial kernel free parameter

r - a double, the soft margin cost function parameter

degree - a double, the degree of the polynomial kernel

Method Detail

clone

public PolynomialKernel clone()

Clones a PolynomialKernel kernel.

Specified by:

clone in class Kernel

Returns:

a clone of the PolynomialKernel kernel

setParameters

public void setParameters(double... kParams)

Sets the parameters for the polynomial kernel.

Overrides:

setParameters in class Kernel

Parameters:

kParams - a double array of length 3 containing parameter values: kParams[0]=\(\gamma\), kParams[1]=r, and kParams[2]=d.

Default: kParams[0]=\(\gamma\)=1.0, kParams[1]=r=0, and kParams[2]=d=1.

kernelFunction

public double kernelFunction(DataNode[] x,
                             DataNode[] y)

Calculates the kernel function between two DataNodes.

Specified by:

kernelFunction in class Kernel

Parameters:

x - a DataNode array

y - a DataNode array

Returns:

a double, the kernel function evaluated at x and y

kernelFunction

public double kernelFunction(DataNode[][] x,
                             int i,
                             int j)

Calculates the kernel function between two DataNodes.

Specified by:

kernelFunction in class Kernel

Parameters:

x - a DataNode matrix

i - an int, the index of the first DataNode, x[i]

j - an int, the index of the second DataNode, x[j]

Returns:

a double, the kernel function evaluated at x[i] and x[j]