Radial basis (Gaussian) kernel

$$k(x,y) = \exp(-\|x-y\|^2/(2\sigma^2))$$ This takes the bandwidth, not the rate; the equivalent \(\gamma = 1/(2\sigma^2)\) is returned so the two conventions cannot be confused.

Usage

Rbfk(x, y, sigma)

Arguments

x, y

Vectors of the same length.

sigma

Bandwidth, positive.

Value

Named list with estimate, value, sq_distance, distance, sigma, gamma, method.

References

Standard kernel method; no single owning source.

Examples

Rbfk(c(0, 0), c(3, 4), 2)
#> $estimate
#> [1] 0.04393693
#> 
#> $value
#> [1] 0.04393693
#> 
#> $sq_distance
#> [1] 25
#> 
#> $distance
#> [1] 5
#> 
#> $sigma
#> [1] 2
#> 
#> $gamma
#> [1] 0.125
#> 
#> $method
#> [1] "radial basis (Gaussian) kernel"
#>