# Temporal Multi Dimensional Scaling

Let's say I apply a multidimensional scaling(MDS) to a dynamic dataset of $n$ points (eg, time series). At each step I will obtain a projection (in 2/3D) of the $n$ points. If nothing meaningful happen it should be similar, if there are some changes, the projection should look different. However, since, to the best of my knowledge, MDS techniques would return positions with arbitrary translation and reflection, it can be hard to monitor from a step to another if the projections are the same.

For example, in the picture below, points red and violet should be at the same place than the 'corresponding' blue,orange,green.

My question is thus: Are there specific techniques for applying MDS in a temporal setting where one wants to link the different projections?

I have cooked some naive solution by estimation a rotation o reflexion between two successive steps such that the projections look similar. But that is not a 'proper' solution as I mixed the method rotation o reflexion with some of 'real' changes in the projection.

Any suggestions?

• MDS is based on dissmilarity matrix which it tries to approximate. so why don't you just compare the difference of dissimilarity matrix using e.g. Frobenius norm? – Xiaoxiong Lin Feb 19 at 15:03