rde_loocv: Relevant Dimension Estimation (RDE) by Leave-One-Out...
In rdetools: Relevant Dimension Estimation (RDE) in Feature Spaces

Description Usage Arguments Details Value Author(s) References See Also Examples

The function estimates the relevant dimension in feature space by leave-one-out cross-validation. It's also able to calculate a denoised version of the labels and to estimate the noise level in the data set.

rde_loocv(K, y,
          est_y = FALSE,
	  alldim = FALSE,
	  est_noise = FALSE,
	  regression = FALSE,
	  nmse = TRUE,
	  dim_rest = 0.5)

`K`	kernel matrix of the inputs (e.g. rbf kernel matrix)
`y`	label vector which contains the label for each data point
`est_y`	set this to TRUE if you want a denoised version of the labels
`alldim`	if this is TRUE denoised labels for all dimensions are calculated (instead of only for relevant dimension)
`est_noise`	set this to TRUE if you want an estimated noise level
`regression`	only interesting if one of `est_y`, `alldim`, `est_noise` is TRUE. Set this to TRUE if you want to force the function to handle the data as data for a regression problem. If you leave this FALSE, the function will try to determine itself whether this is a classification or regression problem.
`nmse`	only interesting if `est_noise` is TRUE and the function is handling the data as data of a regression problem. If you leave this TRUE, the normalized mean squared error is used for estimating the noise level, otherwise the conventional mean squared error.
`dim_rest`	percantage of leading dimensions to which the search for the relevant dimensions should be restricted. This is needed due to numerical instabilities. 0.5 should be a good choice in most cases (and is also the default value)

If est_noise or alldim are TRUE, a denoised version of the labels for the relevant dimension will be returned even if est_y is FALSE (so e.g. if you want denoised labels and noise approximation it is enough to set est_noise to TRUE).

`rd`	estimated relevant dimension
`err`	loo-cv error for each dimension (the position of the minimum is the relevant dimension)
`yh`	only returned if `est_y`, `alldim` or `est_noise` is TRUE, contains the denoised labels
`Yh`	only returned if `alldim` is TRUE, matrix with denoised labels for each dimension in each column
`noise`	only returned if `est_noise` is TRUE, contains the estimated noise level
`kpc`	kernel pca coefficients
`eigvec`	eigenvectors of the kernel matrix
`eigval`	eigenvalues of the kernel matrix
`tcm`	always FALSE; used to tell other functions that loo-cv method was used

Jan Saputra Mueller

M. L. Braun, J. M. Buhmann, K. R. Mueller (2008) \_On Relevant Dimensions in Kernel Feature Spaces\_

rde, rde_tcm, estnoise, isregression, rbfkernel, polykernel, drawkpc

## example with sinc data
d <- sincdata(100, 0.1) # generate sinc data
K <- rbfkernel(d$X) # calculate rbf kernel matrix
# rde, return also denoised labels and noise
r <- rde_loocv(K, d$y, est_y = TRUE, est_noise = TRUE)
r$rd # estimated relevant dimension
r$noise # estimated noise
drawkpc(r) # draw kernel pca coefficients