AggregateSVD {GeneSelector} | R Documentation

## Agregation of repeated rankings using the singular value decomposition (SVD)

### Description

A matrix storing all rankings is centered rowwise (=genewise), and then approximated using only the first singular value and the first singular vectors (s. Golub and Van Loan (1983) for details about the SVD). The rowwise mean vector is added afterwards, and the rowwise mean are finally used as aggregation. A weighting scheme giving more weight to top genes is incorporated by an (iteratively) weighted SVD, which is re-computed until convergence. Note that the SVD is closely related to principal component analysis, a standard tool for dimension reduction in high-dimensional datasets.

### Usage

      AggregateSVD(RR, weightscheme = c("original", "iterative"), decay = c("linear", "quadratic", "exponential"), alpha=1)

### Arguments

`RR` | An object of class `RepeatedRanking`
`weightscheme` | If `weightscheme = "original"`, the weights are computed according to the reference ranking `RR@ranking@original`. If `weightscheme = "iterative"`, the weights are intially set to 1 for all genes. After the computation of the SVD and in turn the first aggregation, the weightes are updated according to that aggregation. This process is repeated until convergence.
`decay` | Argument controlling the weight decay of the weights of the summands contributing to the stability measure. If `decay=linear`, then we have weight `1/r` for rank `r`, if `decay=quadratic`, then the weight is `1/r^2` and if `decay=quadratic`, then the weight is `exp(-alpha*r)` where `alpha` is a tuning parameter, specified via the argument `alpha`.
`alpha` | s. `decay`.

### Value

An object of class AggregatedRanking.

### Author(s)

Martin Slawski
Anne-Laure Boulesteix

### References

Golub, G., Van Loan, C. (1983)
Matrix Computations John Hopkins University Press

### See Also

RepeatRanking, AggregateSimple, AggregatePenalty, AggregateMC

### Examples

    ## Load toy gene expression data
    data(toydata)
    ### class labels
    yy <- toydata[1,]
    ### gene expression
    xx <- toydata[-1,]
    ### run RankingTstat
    ordT <- RankingTstat(xx, yy, type="unpaired")
    ### Generate Leave-one-out Foldmatrix
    loo <- GenerateFoldMatrix(y = yy, k=1)
    ### Get all rankings
    loor_ordT <- RepeatRanking(ordT, loo)
    ### aggregate rankings
    agg_svd_ordT <- AggregateSVD(loor_ordT, weightscheme = "iterative", decay = "linear")
    toplist(agg_svd_ordT)

[Package GeneSelector version 2.30.0 Index]