Talk:Multidimensional scaling

Something is missing here
In the section Non-metric multidimensional scaling (NMDS) we find the following:

''In contrast to metric MDS, non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. For NMDS, it is unnecessary to''

The paragraph ends abruptly whereupon the article continues:

''Let (...) be the dissimilarity between points (...). Let (...) be the Euclidean distance between embedded points (...). Now, for each choice of the embedded points (...) and is a monotonically increasing function (...), define the "stress" function:''

I think the part and is a monotonically increasing function could be replaced with the word "let." This sentence seems to describe the caracteristics of the stress function, which is a good idea, but perhaps better demoted until the stress function has actually been defined. 93.160.68.190 (talk) 07:10, 7 August 2023 (UTC)


 * The other sentence,
 * Now, for each choice of the embedded points (...) and is a monotonically increasing function (...), define the "stress" function:
 * I am thinking now it would suffice to delete the word 'is' like this:
 * Now, for each choice of the embedded points (...) and a monotonically increasing function (...), define the "stress" function: 85.191.125.4 (talk) 09:30, 7 August 2023 (UTC)

Stress Formula in mMDS vs NMDS
I am not that deep into the topic, but as far as I see it, the formulas for stress as presented in the sections of metric and non-metric MDS are not specific to their section other than the NMDS formula using the function f.

Especially, as far as I see it, the divisor used in the formula in the NMDS section (sum d^_ij²) is simply normalization that makes it robust vs scaling and could as well be present in the section of mMDS.

Maybe the presentation should be reworked, the formulas set in a unified format (no ||x_i-x_j|| anymore) for better comparison, and the possibility of weights w_ij added.

As I am not that deep into the topic, I am hesitant to do any direct edit here, though.

2001:638:208:3606:39F0:EDA6:A8CD:80 (talk) 14:23, 13 June 2024 (UTC)