Interpret multidimensional scaling plot I have data with 4 observations and 24 variables. To understand the underlying relationship I performed Multi-Dimensional Scaling (MDS), and got a plot like this:

Now the issue is with the correct interpretation of the plot. I understand the two axes (i.e., the x-axis and y-axis) imply the variation in data along the two principal components. But, my specific doubts are:


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*Should I infer that points 1 and 3 vary along dimension-1 only and there is no relationship between them in dimension-2?

*Similarly, should I infer points 1 and 2 along dimension-2 only?

*How should I explain the relationship of point 4 with the rest of the points?

 A: Despite having 24 original variables, you can perfectly fit the distances amongst your data with 3 dimensions because you have only 4 points.  It is possible that your points lie exactly on a 2D plane through the original 24D space, but that is incredibly unlikely, in my opinion.  It is reasonable to imagine that the variation on the third dimension is inconsequential and/or unreliable, but I don't have any information about that.  I am assuming that there is a third dimension that isn't represented in your plot.  


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*You can infer that 1 and 3 do not vary on dimension 2, but you have no information here about whether they vary on dimension 3.  Thus, you cannot necessarily assume that they vary on dimension 1 only.  

*Likewise, you can infer that 1 and 2 do not vary on dimension 1, but again you have no information about whether they vary on dimension 3.  So, you cannot necessarily assume that they vary on dimension 2 only.  

*Point 4 differs from 1, 2, and 3 on both dimensions 1 and 2. Its relationship to them on dimension 3 is unknown.  Ignoring dimension 3 for a moment, you could think of point 4 as the medoid of your dataset.  

A: Sorry to necro, but found this through a search and thought I could help others.
The correct answer is that there is no interpretability to the MDS1 and MDS2 dimensions with respect to your original 24-space points.
This is because MDS performs a nonparametric transformations from the original 24-space into 2-space.
The only interpretation that you can take from the resulting plot is from the distances between points. The further away two points are the more dissimilar they are in 24-space, and conversely the closer two points are the more similar they are in 24-space. 
