General procedure to assess goodness of fit rather than explained variance ratio.

[aron0093]

1. It isn't easy to come up with a generic procedure for this calculation in the former scenario since many methods further process the expression matrix internally without reporting it.

2. The model output can be arbitrarily worse for non-linear methods and produce negative values for this evaluation.

For k selection (assuming good model fit) we can get a knee plot by plotting the variance explained by each component w.r.t. total modeled variance. This evaluation will focus on selecting the appropriate k while we can introduce a different evaluation to assess goodness of fit.

Or we could come up with a generalisable evaluation (e.g. information based) to compute goodness of fit that can also be used for k selection.