Gamma hyperparameter estimation (RBF kernel)

This function returns an estimation of the optimum value for the gamma hyperparameter (required by the RBF kernel function) using different heuristics:

D criterion

It returns the inverse of the number of features in X.

Scale criterion

It returns the inverse of the number of features, normalized by the total variance of X.

Quantiles criterion

A range of values, computed with the function `kernlab::sigest()`.

Usage

estimate_gamma(X)

Arguments

X

Matrix or data.frame that contains real numbers ("integer", "float" or "double").

Value

A list with the gamma value estimation according to different criteria.

Examples

data <- matrix(rnorm(150),ncol=50,nrow=30)
gamma <- estimate_gamma(data)
gamma
#> $d_criterion
#> [1] 0.02
#> 
#> $scale_criterion
#> [1] 0.02081624
#> 
#> $quantiles_criterion
#>         90%         50%         10% 
#> 0.006118612 0.011947701 0.029490575 
#> 
K <- RBF(data, g = gamma$scale_criterion)
K[1:5,1:5]
#>            [,1]       [,2]       [,3]       [,4]      [,5]
#> [1,] 1.00000000 0.05736523 0.42652586 0.06450117 0.1484147
#> [2,] 0.05736523 1.00000000 0.06112368 0.01671617 0.2770090
#> [3,] 0.42652586 0.06112368 1.00000000 0.46120814 0.2436350
#> [4,] 0.06450117 0.01671617 0.46120814 1.00000000 0.1809315
#> [5,] 0.14841470 0.27700897 0.24363504 0.18093149 1.0000000