Compute probability of each element in each column of a m x n matrix.

Hello Friends,

I have a m x n matrix. I want to compute the probability of each element occurring in a column. I want to do it for each column.

For instance, suppose we have a 3 x 4 matrix:

A = [1 1 3 2; 2 3 0 2; 3 1 0 2];

Then, I would like to have the following matrix of probabilities: _P(A) = [ 1/3 2/3 1/3 1; 1/3 1/3 2/3 1; 1/3 2/3 2/3 1];_

Here, entries in P(A) are the probabilities of each element within the column.

For the 1st column: p(1) = p(2) = p(3) = 1/3

For the 2nd column: p(1) = 2/3, p(3) = 1/3

For the 3rd column: p(3) = 1/3, p(0) = 2/3

For the 4th column: p(2) = 3/3 = 1.

Please advise.

Answer 1

[hello_world]

I found the solution of my own problem posted above. Though, thanks for your kind help. I will still appreciate different ways to solve it specially with hist(), and histc(). Here is my solution to this problem:

[r, c] = size(A);

y = zeros(r,c);
p = zeros(r,c);

for i = 1:c                               %Looping through the column.
    for j = 1:r                           %Looping through the row in that that column.
        y(j,i) = sum(A(:,[i]) == A(j,i)); %Compare each column of the matrix with the entries in that column.
        p(j,i) = y(j,i)/r;                %Probability of each entry of a column within that column.  
    end
end

Answer 2

[Sukumar GV]

You can use the following.

Suppose Matrix is X

[a, b] = hist (X, unique(X))

a/size(X,1)

each row represents item and each column represents the dimension

Answer 3

[Yu Jiang]

One possible but most likely not optimal way is to use the function "find" to count the number of occurrence of a particular number. For example,

[r,c] = size(A); % get the column of A
nr = 0:3;  %range of the numbers
P = zeros(r,c); % create a matrix to store the probabilities
for j = 1:c   % check each row
    for i = 1:length(nr)   % check each particular number
        P(i,j) = length(find(A(:,j) == nr(i)))/r;  % count the occurrence
    end
end

[hello_world]

Hi Yu Jiang,

Thanks you for your kind help. In my case, I do not have a range of the number as you specified 'nr'. In fact each column is a real number (-ve, +ve, 0, decimal point). I can not even see what is the minimum and maximum number as the column is quite large.

I was wondering if I could use histogram for this purpose, e.g., histc() command.

[Hugo]

The range of the numbers refers to the minimum and the maximum number in your matrix. You can just replace the line nr=0:3; with nr=min(A(:)):max(A(:));

This will only work, of course, if A contains only integers. If it doesn't, things get a little more complicated. Hope this helps.

[hello_world]

Thanks for help, though entries in my matrix are not integers. They are real number.

By making your suggested improvement, it gives me a 6 x 5 matrix of probabilities for a 3 x 5 size of matrix A. How is it possible? Should not I get a 3 x 5 size probability matrix instead?