How to move larger values close to matrix diagonal in a correlation matrix

Question

I have a correlation matrix X of five elements(C1,C2,C3,C4,C5)

      C1    C2    C3     C4   C5  

 C1    *     1     0     1     0
 C2    1     *     0              


        

Answer 1

What you're looking for is probably the reverse Cuthill-McKee algorithm (RCM), which pretty much does what you want: for a given matrix it finds a permutation that tends to have its non-zero elements closer to the diagonal. There's a built-in function symrcm in MATLAB that does just that.

So assuming that X is your matrix, you can do the following:

p = symrcm(X);
Xnew = X(p, p);

Xnew is the new reordered matrix, and p is the new row/column order.

Example

Let's create a matrix first:

X = [10 0 0 7 0; 3 20 0 0 11; 0 0 30 0 29; 12 7 0 40 0; 0 33 0 0 50]

Now let's reorder it:

p = symrcm(X);
Xnew = X(p, p)

The result is:

Xnew =    
    40    12     7     0     0
     7    10     0     0     0
     0     3    20    11     0
     0     0    33    50     0
     0     0     0    29    30

Seems right.