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DRR

drr

Dimensionality Reduction via Regression

Description

drr Implements Dimensionality Reduction via Regression using Kernel Ridge Regression.

Usage

drr(
  X,
  ndim = ncol(X),
  lambda = c(0, 10^(-3:2)),
  kernel = "rbfdot",
  kernel.pars = list(sigma = 10^(-3:4)),
  pca = TRUE,
  pca.center = TRUE,
  pca.scale = FALSE,
  fastcv = FALSE,
  cv.folds = 5,
  fastcv.test = NULL,
  fastkrr.nblocks = 4,
  verbose = TRUE
)

Arguments

`X`	input data, a matrix.
`ndim`	the number of output dimensions and regression functions to be estimated, see details for inversion.
`lambda`	the penalty term for the Kernel Ridge Regression.
`kernel`	a kernel function or string, see `kernel-class` for details.
`kernel.pars`	a list with parameters for the kernel. each parameter can be a vector, crossvalidation will choose the best combination.
`pca`	logical, do a preprocessing using pca.
`pca.center`	logical, center data before applying pca.
`pca.scale`	logical, scale data before applying pca.
`fastcv`	if `TRUE` uses `fastCV`, if `FALSE` uses `CV` for crossvalidation.
`cv.folds`	if using normal crossvalidation, the number of folds to be used.
`fastcv.test`	an optional separate test data set to be used for `fastCV`, handed over as option `test` to `fastCV`.
`fastkrr.nblocks`	the number of blocks used for fast KRR, higher numbers are faster to compute but may introduce numerical inaccurracies, see `constructFastKRRLearner` for details.
`verbose`	logical, should the crossvalidation report back.

Details

Parameter combination will be formed and cross-validation used to select the best combination. Cross-validation uses CV or fastCV.

Pre-treatment of the data using a PCA and scaling is made α = Vx. the representation in reduced dimensions is

y_i = α - f_i(α_1, …, α_{i-1})

then the final DRR representation is:

r = (α_1, y_2, y_3, …,y_d)

DRR is invertible by

α_i = y_i + f_i(α_1,α_2, …, alpha_{i-1})

If less dimensions are estimated, there will be less inverse functions and calculating the inverse will be inaccurate.

Value

A list the following items:

"fitted.data" The data in reduced dimensions.
"pca.means" The means used to center the original data.
"pca.scale" The standard deviations used to scale the original data.
"pca.rotation" The rotation matrix of the PCA.
"models" A list of models used to estimate each dimension.
"apply" A function to fit new data to the estimated model.
"inverse" A function to untransform data.

References

Laparra, V., Malo, J., Camps-Valls, G., 2015. Dimensionality Reduction via Regression in Hyperspectral Imagery. IEEE Journal of Selected Topics in Signal Processing 9, 1026-1036. doi:10.1109/JSTSP.2015.2417833

Examples

tt <- seq(0,4*pi, length.out = 200)
helix <- cbind(
  x = 3 * cos(tt) + rnorm(length(tt), sd = seq(0.1, 1.4, length.out = length(tt))),
  y = 3 * sin(tt) + rnorm(length(tt), sd = seq(0.1, 1.4, length.out = length(tt))),
  z = 2 * tt      + rnorm(length(tt), sd = seq(0.1, 1.4, length.out = length(tt)))
)
helix <- helix[sample(nrow(helix)),] # shuffling data is important!!
system.time(
drr.fit  <- drr(helix, ndim = 3, cv.folds = 4,
                lambda = 10^(-2:1),
                kernel.pars = list(sigma = 10^(0:3)),
                fastkrr.nblocks = 2, verbose = TRUE,
                fastcv = FALSE)
)

## Not run: 
library(rgl)
plot3d(helix)
points3d(drr.fit$inverse(drr.fit$fitted.data[,1,drop = FALSE]), col = 'blue')
points3d(drr.fit$inverse(drr.fit$fitted.data[,1:2]),             col = 'red')

plot3d(drr.fit$fitted.data)
pad <- -3
fd <- drr.fit$fitted.data
xx <- seq(min(fd[,1]),       max(fd[,1]),       length.out = 25)
yy <- seq(min(fd[,2]) - pad, max(fd[,2]) + pad, length.out = 5)
zz <- seq(min(fd[,3]) - pad, max(fd[,3]) + pad, length.out = 5)

dd <- as.matrix(expand.grid(xx, yy, zz))
plot3d(helix)
for(y in yy) for(x in xx)
  rgl.linestrips(drr.fit$inverse(cbind(x, y, zz)), col = 'blue')
for(y in yy) for(z in zz)
  rgl.linestrips(drr.fit$inverse(cbind(xx, y, z)), col = 'blue')
for(x in xx) for(z in zz)
  rgl.linestrips(drr.fit$inverse(cbind(x, yy, z)), col = 'blue')

## End(Not run)

DRR

Dimensionality Reduction via Regression

v0.0.4

GPL-3 | file LICENSE

Authors

Guido Kraemer [aut, cre]

Initial release

drr