# Relevant Dimension Estimation (RDE) by Leave-One-Out Cross-Validation (LOO-CV)

### Description

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.

### Usage

1 2 3 4 5 6 7 |

### Arguments

`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 |

`nmse` |
only interesting if |

`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) |

### Details

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).

### Value

`rd` |
estimated relevant dimension |

`err` |
loo-cv error for each dimension (the position of the minimum is the relevant dimension) |

`yh` |
only returned if |

`Yh` |
only returned if |

`noise` |
only returned if |

`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 |

### Author(s)

Jan Saputra Mueller

### References

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

### See Also

`rde`

, `rde_tcm`

, `estnoise`

,
`isregression`

, `rbfkernel`

, `polykernel`

, `drawkpc`

### Examples

1 2 3 4 5 6 7 8 | ```
## 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
``` |