If i have two binary matrix how can calculate the similarities between them

If i have (n,m) matrix M

        M =     [ 1 0 1 1 0 1
                  0 1 1 0 0 1
                  0 0 1 0 1 0
                  1 1 1 1 0 0]

And after some operation i found this two matrix which every one shows the number of group of ones in each row and in each column

             M_row = [ 1 2 1
                       2 1 0
                       1 1 0
                       4 0 0 ]

            M_col = [ 1 1 0 1 0
                      1 1 4 1 2 ]

After that generate a random matrix X in same size of M and then calculate the X_row and X_col like Matrix M

After that i need some way or a function to determine the similarities between M and X using the M_row ,M_col , X_row and X_col

Answer 1

[Walter Roberson]

if isequal(M_row, X_row) && isequal(M_col, X_col)
  similarity = 1;
else
  similarities = {'purple', 'tuba', 'beer', 'tardigrade', 'top quark'};
  similarity = similarities{randi(length(similarities))};
end

[Firas Al-Kharabsheh]

Can you give me an equation to measure the similarities ?

[Firas Al-Kharabsheh]

what did you mean by 'purple', 'tuba', 'beer', 'tardigrade', 'top quark'?

[Firas Al-Kharabsheh]

i want a function give the value because the X matrix will be change

[Walter Roberson]

Well, here it is in function form then:

function similarity = compare_Mx(M_row, M_col, X_row, X_col)
  if isequal(M_row, X_row) && isequal(M_col, X_col)
    similarity = 1;
  else
    similarities = {'purple', 'tuba', 'beer', 'tardigrade', 'top quark'};
    similarity = similarities{randi(length(similarities))};
  end
end

The result of the function is the similarity level that is computed. The function meets all of your specifications for how similarity is to be computed. If it does not produce the answer that you want, then perhaps you should change your specification of "similarity".