Why SVD "cumulative variance plot" is not scaled to 100%

jacobcybulski

When using PCA the cumulative variance plot, among many things, allows determining if your visualisation in PC1xPC2 reliably depicts your data (shows large part of variance). In SVD this plot is called "Cumulative Proportion of Single Values" and it is not scaled to 100%. Is there any reason for SVD not to represent variance, is it not variance that is depicted in the plot?

Jacob

Telcontar120

@jacobcybulski interesting, since PCA is a special case of SVD, but I am not sure what it is being scaled to in the exhibits presented in RapidMiner.  @mschmitz any idea what the denominator is?

jacobcybulski

Thanks @Telcontar120 , I agree that there is some discrepancy between PCA and SVD. If SVD indeed shows cumulative variance, the units would not need to scale to 100. However, a scaled cumulative variance is the expected norm, especially that analytic decisions are being made around the chart.

MartinLiebig

Hi @Telcontar120 ,

i am honored that you think that I know those things, but i don't. What i can say is:

/**
 * This operator performs a Singular Value Decomposition (SVD) of the data The user can specify the
 * number of target dimensions operator outputs a {@link SVDModel}. With the
 * <code>ModelApplier</code> you can transform the features.
 *
 * @author Sebastian Land
 */

So this is more @land thing.

Best,

Martin