I have a matrix X where the rows denote the cases and the columns the variables. I use a standard row-metric preserving biplot in order to represent the cases in a subspace. If I wanted to add a supplementary point (i.e. a row) I can simply project the point it into that space.
But, how can I optimally fit a point into the biplot if the supplementary point does only have values on some of the variables, i.e. if it only uses subset of the variables the biplot is constructed from? How can I add such a row point to a biplot?