```java.lang.Object
```
All Implemented Interfaces:
KernelFunction, Proximity<Vector>, Serializable

`public class GaussianRadialBasisKernelextends Objectimplements KernelFunction, Serializable`

A `GaussianRadialBasisKernel` provides a kernel based on a Gaussian radial basis function with a fixed variance parameter. As a kernel function, it unfolds into an infinite-dimension Hilbert space.

The radial basis kernel function of radius `r` is defined between vectors `v1` and `v2` as follows:

``` rbf(v1,v2) = exp(- r * distance(v1,v2)2)
```
where `distance(v1,v2)` is the Euclidean distance, as defined in the class documentation for `EuclideanDistance`. In this formulation, the radius `r` is related to the variance `σ2` by:
` r = 1/(2 * σ2)`

Since:
LingPipe3.1
Version:
3.8
Author:
Bob Carpenter
Serialized Form

Constructor Summary
`GaussianRadialBasisKernel(double radius)`
Construct a Gaussian radial basis kernel with the specified radius of influence.

Method Summary
` double` ```proximity(Vector v1, Vector v2)```
Returns the result of applying this Guassian radial basis kernel to the specified vectors.
` String` `toString()`
Returns a string-based representation of this kernel function, including the kernel type and radius.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

`public GaussianRadialBasisKernel(double radius)`
Construct a Gaussian radial basis kernel with the specified radius of influence.

Parameters:
`radius` - The radius of influence for the kernel.
Method Detail

### proximity

```public double proximity(Vector v1,
Vector v2)```
Returns the result of applying this Guassian radial basis kernel to the specified vectors. See the class documentation above for a full definition.

Specified by:
`proximity` in interface `KernelFunction`
Specified by:
`proximity` in interface `Proximity<Vector>`
Parameters:
`v1` - First vector.
`v2` - Second vector.
Returns:
Kernel function applied to the two vectors.
Throws:
`IllegalArgumentException` - If the vectors are not of the same dimensionality.

### toString

`public String toString()`
Returns a string-based representation of this kernel function, including the kernel type and radius.

Overrides:
`toString` in class `Object`
Returns:
A string representing this kernel.