Dear list member,
Recently I am learning about multi-dimensional scaling myself.
May I ask about pointers to the literature on the following questions?
As I am pretty new to MDS, please accept my apology if they sound standard
to you. I am mostly interested in metric MDS, in particular metric least
square scaling.
1. What is the state of the art for the additive constant problem?
2. What is the best way to convert a similarity matrix to a
dissimilarity matrix? In addition to the additive constant
problem, what else can go wrong?
3. Suppose I have performed MDS on a set of n by n dissimilarity
matrix. Now I have a new item $z$, and I know its dissimilarity with
all existing n items. If I want to do MDS on these (n+1) items,
must I recalculate everything from scratch? Or is there any
approximation method to find the co-ordinate for $z$?
4. Has anyone studied the "inverse-mapping" problem of MDS, that is,
given an arbitrary point in the projected space, we try to
recover the corresponding item? Obviously, this requires
knowledge on the space the items are located, in addition to
the dissimilarity matrix.
Thank you for your advice.
Best regards,
Martin
