biplot understanding

>> x=[1 2 3 4 5 6;1 2 3 4 5 6]'

x =

       1     1
       2     2
       3     3
       4     4
       5     5
       6     6

>> biplot(x)

>> x=[1 2 3 4 5 6;1 2 3 4 5 -6]'

x =

       1     1
       2     2
       3     3
       4     4
       5     5
       6    -6

>> biplot(x)

Iam unable understand biplot for the above two cases. What the second biplot is doing there ?

Answer 1

[Wayne King]

Hi, In the first biplot both component 1 and component 2 (the columns of your matrix) are in the same direction and magnitude.

In the second example, biplot() makes the largest magnitude coefficient (element) in each column positive. That is the sign convention. So the -6 in the second column becomes positive and all the other elements in the 2nd column change sign to be negative.

That does not affect the interpretation, which demonstrates that x(end,1) and x(end,2) differ from the relationship between x(1:end-1,1) and x(1:end-1,2)

Wayne

[Raviteja]

May I know, why only it change sign conversion for the maximum coefficient (element) in a cloumn ? I mean what advantage we got from this?

[Wayne King]

I suspect that since the inputs to biplot() are typically principal component coefficients or factor loadings, basing the signs on the largest magnitude principal component coefficient or factor loading makes a lot of sense. Because you change all the signs in the vector accordingly, the interpretation is not affected.

[Raviteja]

Thanks Wayne!