6
$\begingroup$

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:

enter image description here

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:

  1. Should I infer that points 1 and 3 vary along dimension-1 only and there is no relationship between them in dimension-2?
  2. Similarly, should I infer points 1 and 2 along dimension-2 only?
  3. How should I explain the relationship of point 4 with the rest of the points?
Improve this question
$\endgroup$
2
  • $\begingroup$ Unclear what you're asking. What are your specific concerns? What makes you fear that you cannot interpret an MDS plot like a usual scatterplot? $\endgroup$
    – ttnphns
    Nov 13, 2015 at 8:38
  • $\begingroup$ I admit that I am not interpreting this as a usual scatter plot. I thought that plotting data from two principal axis might need some different interpretation. So, should I take it exactly as a scatter plot while interpreting ? $\endgroup$
    – Haroon Lone
    Nov 13, 2015 at 11:33

2 Answers 2

Reset to default
6
$\begingroup$

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.

  1. 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.
  2. 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.
  3. 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.
Improve this answer
$\endgroup$
1
$\begingroup$

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.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.