warpNorm | R Documentation |
Given warpings for ordinal inputs.
warpNorm
warpUnorm
warpPower
warpSpline1
warpSpline2
The format is a list of 6:
$ fun : the warping function. The second argument is the vector of
parameters. The function returns a numeric vector with an attribute
"gradient"
giving the derivative w.r.t. the parameters.
$ parNames : names of warping parameters (character vector).
$ parDefault: default values of warping parameters (numeric vector).
$ parLower : lower bounds of warping parameters (numeric vector).
$ parUpper : upper bounds of warping parameters (numeric vector).
$ hasGrad : a boolean equal to TRUE
if gradient
is
supplied as an attribute of fun
.
See covOrd
for the definition of a warping in this
context. At this stage, two warpings corresponding to cumulative
density functions (cdf) are implemented:
Normal distribution, truncated to [0,1]
:
F(x) = [N(x) -
N(0)] / [N(1) - N(0)]
where N(x) = \Phi([x - \mu] /
\sigma)
is the cdf of the normal
distribution with mean \mu
and standard deviation
\sigma
.
Power distribution on [0, 1]
: F(x) = x^{pow}
.
Furthermore, a warping corresponding to unnormalized Normal cdf is implemented,
as well as spline warpings of degree 1 and 2.
Splines are defined by a sequence of k
knots between 0 and 1. The first knot is 0, and the last is 1.
A spline warping of degree 1 is a continuous piecewise linear function.
It is parameterized by a positive vector of length k-1
, representing the increments at knots.
A spline warping of degree 2 is a non-decreasing quadratic spline. It is obtained by integrating a spline of degree 1.
Its parameters form a positive vector of length k
, representing the derivatives at knots. The implementation relies on the function scalingFun1d
of DiceKriging
package.
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