[R] Plotting MDS (multidimensional scaling)

Mario Valle mvalle at cscs.ch
Sun Apr 3 07:37:31 CEST 2011

Also try the asp parameter in plot.

plot(fit2$points, xlab="Coordinate 1", ylab="Coordinate 2",main="Metric 
text(fit2$points, labels = c('A','B','C','D'), cex=1)

Hope it helps

On 02-Apr-11 22:07, Daniel Malter wrote:
> Hi,
> I just encountered what I thought was strange behavior in MDS. However, it
> turned out that the mistake was mine. The lesson learned from my mistake is
> that one should plot on a square pane when plotting results of an MDS. Not
> doing so can be very misleading. Follow the example of an equilateral
> triangle below to see what I mean. I hope this helps others to avoid this
> kind of headache.
> Let's say I have an equilateral triangle. Then, the three Euclidean
> distances between points A, B, and C  are all equal. That is,
> dist(AB)=dist(AC)=dist(BC). Let the points A, B, and C have
> (x,y)-coordinates  (0,0), (2,0), and (1,sqrt(3)). Then, MDS should reproduce
> an equilateral triangle, which it does if there are only three points.
> require(MASS)
> x=c(0,2,1,0,0,sqrt(3))
> dim(x)=c(3,2)
> d1=dist(x)
> fit1<-isoMDS(d1)
> plot(fit1$points, xlab="Coordinate 1", ylab="Coordinate 2",
>    main="Metric MDS",type="n")
> text(fit1$points, labels = c('A','B','C'), cex=1)
> So far so good, until I add more points. Now assume, I add a fourth point D
> at {0,2*sqrt(3)}. This produces the rectangular triangle ABD with
> hypothenuse BD that encompasses the smaller triangle ABC such that C lies in
> the middle between B and D. Then, MDS should reproduce the rectangular
> triangle ABD and the equilateral triangle ABC within it. However, even
> though distance matrix d2 below still indicates that ABC is an equilateral
> triangle, the plot of the MDS does not confirm this.
> x=c(0,2,1,0,0,0,sqrt(3),2*sqrt(3))
> dim(x)=c(4,2)
> d2=dist(x)
> fit2<-isoMDS(d2)
> plot(fit2$points, xlab="Coordinate 1", ylab="Coordinate 2",
>    main="Metric MDS",type="n")
> text(fit2$points, labels = c('A','B','C','D'), cex=1)
> The reason for this is that the dimension of the plot is automatically
> scaled to fit the points. This distorts the visual impression of the
> distances, angular relationships, and relative locations. If you plot on a
> square pane, however, peace and order are restored in the galaxy.
> plot(fit2$points, xlab="Coordinate 1", ylab="Coordinate 2",
>    main="Metric MDS",type="n",xlim=c(-3,3),ylim=c(-3,3))
> text(fit2$points, labels = c('A','B','C','D'), cex=1)
> Best,
> Daniel
> --
> View this message in context: http://r.789695.n4.nabble.com/Plotting-MDS-multidimensional-scaling-tp3422670p3422670.html
> Sent from the R help mailing list archive at Nabble.com.
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Ing. Mario Valle
Data Analysis and Visualization Group            | http://www.cscs.ch/~mvalle
Swiss National Supercomputing Centre (CSCS)      | Tel:  +41 (91) 610.82.60
v. Cantonale Galleria 2, 6928 Manno, Switzerland | Fax:  +41 (91) 610.82.82

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