R Normalize eigenvectors in spectral clustering then plot

Question

I am following this http://www.pnas.org/content/suppl/2008/12/22/0802806106.DCSupplemental/0802806106SI.pdf to achieve spectral clustering on my correlation matrix. I have calculated eigenvalues/vectors and have chosen the k-most (k=5) significant pairs. The resulting matrix looks like this:

    V1      V2      V3      V4      V5
-0.033  -0.099  -0.046  -0.014  -0.013
-0.010   0.012   0.069   0.087   0.002
 0.010  -0.002   0.114  -0.053  -0.012
0.0023   0.001  -0.013  -0.006  -0.005
 0.004   0.054  -0.011   0.090  -0.049

Now I need to "normalize each row to unit length". How do I go about that? From what I understand, I calculate the length of each row by taking the squareroot of the sum of each value in the row squared as |a| then divide each value in the row by |a|?

If that's the case, how then would I plot these 5 values in the Euclidean Space? 5D plot? Most resources on the web I've found to do with normalizing to unit length deal with x,y,z and can be plotted on a 3-D plot.

Thanks.

Answer 1

If your assumption is correct, you want

df_rn <- df / rowSums(sqrt(df^2))
rowSums(df_rn^2)
[1] 1 1 1 1 1

so all rows are now normalized by their l2 (euclidean) lengths.

Not much can be said about plotting in 5d: it is impossible. Usually 2d (rarely - 3d) projections are drawn. The question of projection plane is open; it depends on what are you trying to show.