This article is within the scope of WikiProject Marketing & Advertising, a collaborative effort to improve the coverage of
Marketing on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.Marketing & AdvertisingWikipedia:WikiProject Marketing & AdvertisingTemplate:WikiProject Marketing & AdvertisingMarketing & Advertising articles
This article has been given a rating which conflicts with the
project-independent quality rating in the banner shell. Please resolve this conflict if possible.
This article is within the scope of
WikiProject Measurement, a project which is currently considered to be defunct.MeasurementWikipedia:WikiProject MeasurementTemplate:WikiProject MeasurementMeasurement articles
This article is within the scope of WikiProject Psychology, a collaborative effort to improve the coverage of
Psychology on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.PsychologyWikipedia:WikiProject PsychologyTemplate:WikiProject Psychologypsychology articles
This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of
statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of
mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
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)reply
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:
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.