MercerKernel

All Superinterfaces:

java.io.Serializable, java.util.function.ToDoubleBiFunction<T,T>

All Known Implementing Classes:

BinarySparseGaussianKernel, BinarySparseHyperbolicTangentKernel, BinarySparseLaplacianKernel, BinarySparseLinearKernel, BinarySparseMaternKernel, BinarySparsePolynomialKernel, BinarySparseThinPlateSplineKernel, GaussianKernel, HellingerKernel, HyperbolicTangentKernel, LaplacianKernel, LinearKernel, MaternKernel, PearsonKernel, PolynomialKernel, ProductKernel, SparseGaussianKernel, SparseHyperbolicTangentKernel, SparseLaplacianKernel, SparseLinearKernel, SparseMaternKernel, SparsePolynomialKernel, SparseThinPlateSplineKernel, SumKernel, ThinPlateSplineKernel
```
public interface MercerKernel<T>
extends java.util.function.ToDoubleBiFunction<T,T>, java.io.Serializable
```
Mercer kernel, also called covariance function in Gaussian process. A kernel is a continuous function that takes two variables x and y and map them to a real value such that k(x,y) = k(y,x). A Mercer kernel is a kernel that is positive Semi-definite. When a kernel is positive semi-definite, one may exploit the kernel trick, the idea of implicitly mapping data to a high-dimensional feature space where some linear algorithm is applied that works exclusively with inner products. Assume we have some mapping Φ from an input space X to a feature space H, then a kernel k(u, v) = <Φ(u), Φ(v)> may be used to define the inner product in feature space H.
Positive definiteness in the context of kernel functions also implies that a kernel matrix created using a particular kernel is positive semi-definite. A matrix is positive semi-definite if its associated eigenvalues are nonnegative.
We can combine or modify existing kernel functions to make new one. For example, the sum of two kernels is a kernel. The product of two kernels is also a kernel.
A stationary covariance function is a function of distance x − y. Thus it is invariant stationarity to translations in the input space. If further the covariance function is a function only of |x − y| then it is called isotropic; it is thus invariant to all rigid motions. If a covariance function depends only on the dot product of x and y, we call it a dot product covariance function.

Method Summary

All Methods Instance Methods Abstract Methods Default Methods
Modifier and Type	Method and Description
`default double`	`apply(T x, T y)` Kernel function.
`default double`	`applyAsDouble(T x, T y)`
`double[]`	`hi()` Returns the upper bound of hyperparameters.
`double[]`	`hyperparameters()` Returns the hyperparameters for tuning.
`default Matrix`	`K(T[] x)` Computes the kernel matrix.
`default Matrix`	`K(T[] x, T[] y)` Returns the kernel matrix.
`double`	`k(T x, T y)` Kernel function.
`default Matrix[]`	`KG(T[] x)` Computes the kernel and gradient matrices.
`double[]`	`kg(T x, T y)` Computes the kernel and its gradient over hyperparameters.
`double[]`	`lo()` Returns the lower bound of hyperparameters.
`MercerKernel<T>`	`of(double[] params)` Returns the same kind kernel with the new hyperparameters.

- Method Detail
  - k
```
double k(T x,
         T y)
```
    Kernel function.
  - kg
```
double[] kg(T x,
            T y)
```
    Computes the kernel and its gradient over hyperparameters.
  - apply
```
default double apply(T x,
                     T y)
```
    Kernel function. This is simply for Scala convenience.
  - applyAsDouble
```
default double applyAsDouble(T x,
                             T y)
```
    Specified by:
    
    applyAsDouble in interface java.util.function.ToDoubleBiFunction<T,T>
  - KG
```
default Matrix[] KG(T[] x)
```
    Computes the kernel and gradient matrices.
    
    Parameters:
    
    x - samples.
    
    Returns:
    
    the kernel and gradient matrices.
  - K
```
default Matrix K(T[] x)
```
    Computes the kernel matrix.
    
    Parameters:
    
    x - samples.
    
    Returns:
    
    the kernel matrix.
  - K
```
default Matrix K(T[] x,
                 T[] y)
```
    Returns the kernel matrix.
    
    Parameters:
    
    x - samples.
    
    y - samples.
    
    Returns:
    
    the kernel matrix.
  - of
```
MercerKernel<T> of(double[] params)
```
    Returns the same kind kernel with the new hyperparameters.
  - hyperparameters
```
double[] hyperparameters()
```
    Returns the hyperparameters for tuning.
  - lo
```
double[] lo()
```
    Returns the lower bound of hyperparameters.
  - hi
```
double[] hi()
```
    Returns the upper bound of hyperparameters.

Interface MercerKernel<T>

Method Summary

Method Detail

k

kg

apply

applyAsDouble

KG

K

K

of

hyperparameters

lo

hi