MDS: amount of explained variance

[ajdapretnar]

What's your use case?

I got a comment from a reviewer, that it would be useful if MDS showed the amount of explained variable. Given that most MDS projections start with PCA initialization, this could perhaps be useful.

What's your proposed solution?

Add info on amount of explained variance. Perhaps to the status bar or to the info box below parameter settings.

Are there any alternative solutions?
Look for the same info with PCA widget?

[ajdapretnar]

Here's what I found as well:

The amount of generalized variance explained by the MDS solution can be expressed as P2 or Mardia criteria. P2 is the ratio of the sum of the eigenvalues over the total sum of the eigenvalues. Mardia criteria squares the numerator and denominator of the P2 values. Both are scaled from 0 to 1, with values closer to 1.0 indicating a good fit.

[janezd]

MDS starts with distances - even if the widget is given a table, it computes distances. Projection is non-linear so even if the original data was table-based, one can't "map" original coordinates to projection. I don't see how one could define explained variance. But then, I may not be an expert in MDS.

Mardia (which I haven't known before) measures the goodness of fit. Scikit doesn't have it, but we could display stress. But I am not sure that Scikit computes stress when using stress majorization. Computing it during updates could be too slow. We could compute it at the end, though.