# rbfkernel: Calculate RBF kernel matrix In rdetools: Relevant Dimension Estimation (RDE) in Feature Spaces

## Description

Calculates the RBF kernel matrix for the dataset contained in the matrix `X`, where each row of `X` is a data point. If `Y` is also a matrix (with the same number of columns as `X`), the kernel function is evaluated between all data points of `X` and `Y`.

## Usage

 `1` ```rbfkernel(X, sigma = 1, Y = NULL) ```

## Arguments

 `X` matrix containing a data point in each row `sigma` kernel width of rbf kernel `Y` leave this NULL if the kernel function should be evaluated between the data points only contained in `X` (which can be regarded as `Y` = `X`) or to a matrix with same number of columns as `X` if you want to evaluate the function between the points of `X` and `Y`

## Details

Each row of `X` must be a data point, i.e. X = (x_1, x_2, ..., x_n). The kernel matrix `K` is then defined as

K = (k(x_i, x_j)), i,j=1,...,n

If `Y` is not NULL and also contains data points in each row, i.e. Y = (y_1, y_2, ..., y_m), the kernel matrix `K` of `X` and `Y` is defined as

K = (k(x_i, x_j)), i=1,...,n, j=1,...,m

In this case, k is the rbf (radial basis function) kernel, which is defined as

k(x, y) = exp(-0.5*\|\|x - y\|\|\^2/sigma)

where x, y are data points and sigma is the rbf kernel width.

## Value

RBF kernel matrix `K` for the given dataset

## Author(s)

Jan Saputra Mueller

`polykernel`, `sincdata`

## Examples

 ```1 2 3``` ```## generate sinc data and calculate rbf kernel matrix with sigma = 1 d <- sincdata(100, noise = 0.1) K <- rbfkernel(d\$X) ```

### Example output

```
```

rdetools documentation built on May 2, 2019, 7:02 a.m.