R: multidimensional scaling

Question

I have a few questions:
1. What is the difference between isoMDS and cmdscale?
2. Can I use an asymmetric matrix?
3. Is there a way to determine the optimal number of measurements (as a result)?

Answer 1

• One of the MDS methods is distance scaling , and it is divided into metric and nonmetric. Another is classical scaling (also called distance geometry by those in bioinformatics). Classic scaling can be done in R using the cmdscale . The Kruskal method of non-metric distance scaling (using the stress function and isotonic regression) can be performed using the isoMDS in the MASS library. The standard classical scaling treatment gives an eigendecomposition problem and, as such, coincides with the PCA if the goal is to reduce dimensionality. On the other hand, distance scaling methods use iterative procedures to achieve a solution.

• If you refer to a distance structure, I assume that you should pass a dist class structure, which is an object with distance information. Either a (symmetric) distance matrix or an object that can be forced to such a matrix using as.matrix (). (As I read in the help, only the lower triangle of the matrix is ​​used, the rest are ignored).

• (for the classical scaling method): one way to determine the dimension of the resulting configuration is to view the eigenvalues ​​of the doubly centered B symmetric matrix (= HAH). A common strategy is to build ordered eigenvalues ​​(or some function of them) against dimension, and then identify the dimension in which the eigenvalues ​​become “stable” (ie, do not change perceptually). In this dimension, we can observe the “elbow”, which shows where stability occurs (for points of n-dimensional space, stability in the graph should occur at dimension n + 1). To simplify the graphical interpretation of the classical scaling solution, we usually choose n small, of the order of 2 or 3.