We have two very similar 8D datasets.
The OLD has 107 records, the NEW has 111 record (107 from the OLD plus 4 additional record).

The NEW dataset download
The OLD dataset download

old <- read.csv(file="old.csv", dec=".", sep=";", header = FALSE)
new <- read.csv(file="new.csv", dec=".", sep=";", header = FALSE)

Sample plots confirming the high compatibility of the two data sets.

par(mfrow = c(1,2), pty="m")

plot(new[,1], new[,2], col="blue", pch=16)
points(old[,1], old[,2], col="red", pch=16)

plot(new[,3], new[,7], col="blue", pch=16)
points(old[,3], old[,7], col="red", pch=16)

enter image description here

Reduction to 2D.

mds.old <- cmdscale(dist(old), k=2)
mds.new <- cmdscale(dist(new), k=2)

Plotting the 2D data clearly shows that the following is true:

mds.new <- mds.old * -1

In other words: the NEW result is reflected in some way comparing to the OLD result.

par(mfrow = c(2,2), pty="m")
plot(mds.old, main="OLD"); grid()
plot(mds.new, main="NEW"); grid()

Plotting the 2D data with the aforementioned modification (mds.new = mds.new * -1)

mds.new <- mds.new * -1
plot(mds.old, main="OLD"); grid()
plot(mds.new, main="NEW"); grid()

enter image description here


What is the reason that the two returned results are so different and scaled by the -1 factor? The OLD and NEW datasets are almost identical and in my opinion, it would be very natural for final results to be very similar to each other.


Because MDS is arbitrary with respect to direction.

In very simple terms, it's roughly like changing a scale from "conservatism" to "liberalism". It's arbitrary whether you say "Joe is high on conservatism" or "Joe is low on liberalism".

In MDS, the interpretation of the dimensions is up to you.

(Similar things happen, for similar reasons, with factor analysis and PCA).

  • 1
    $\begingroup$ If you want to dig deeper and see if the axes of one solution can be rotated to coincide with the axes of another solution, then there is procrustes analysis (search this site, or google ...) $\endgroup$ – kjetil b halvorsen Apr 24 '18 at 11:42

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