# Setting the number of dimensions in an MDS

I have two distance matrixes. The distance matrixes are two topics of a Latent Dirichlet Allocation. The distance is computed based on the probability distribution of the 6 words with the highest weights in each topic. The distance between the objects/brands (BLU, Iphone, Motorola, Samsung) was computed using the Hellinger distance.

dist1

BLU    Iphone  Motorola   Samsung
BLU      0.0000000 0.3396236 0.2101617 0.1973540
Iphone   0.3396236 0.0000000 0.4487546 0.3082306
Motorola 0.2101617 0.4487546 0.0000000 0.1598695
Samsung  0.1973540 0.3082306 0.1598695 0.0000000

dist2

BLU    Iphone  Motorola   Samsung
BLU      0.0000000 0.3396236 0.2879795 0.3225906
Iphone   0.2554609 0.0000000 0.1857408 0.2376081
Motorola 0.2879795 0.4487546 0.0000000 0.1346469
Samsung  0.3225906 0.3082306 0.1346469 0.0000000


My goal is to compare the objects/brands using multidimensional scaling (MDS). My question is how should I set k in the MDS to compare the objects graphically.

For now, I set 'k' to 1:

t1 = cmdscale(dist1, k= 1)
t2 = cmdscale(dist2, k= 1)

comp1 = data.frame(t1, t2)

comp1 = data.frame(t1, t2)
geom_point(aes(x = t1, y = t2, color = row.names(cl1))) +
labs(color = "Brands")


However, I am not sure if this is the right way.

dput(dist1)

structure(list(BLU = c(0, 0.339623559213003, 0.210161658433515,
0.197354039956667), Iphone = c(0.339623559213003, 0, 0.448754641527797,
0.308230635318878), Motorola = c(0.210161658433515, 0.448754641527797,
0, 0.159869524926176), Samsung = c(0.197354039956667, 0.308230635318878,
0.159869524926176, 0)), class = "data.frame", row.names = c("BLU",
"Iphone", "Motorola", "Samsung"))

dput(dist2)

structure(list(BLU = c(0, 0.255460921629425, 0.287979467730357,
0.322590575661145), Iphone = c(0.339623559213003, 0, 0.448754641527797,
0.308230635318878), Motorola = c(0.287979467730357, 0.185740755649388,
0, 0.134646932251419), Samsung = c(0.322590575661145, 0.237608069283077,
0.134646932251419, 0)), class = "data.frame", row.names = c("BLU",
"Iphone", "Motorola", "Samsung"))