Sort columns in a matrix with respect to the means of each column

Hello everybody,

I would like to sort the columns of a matrix with respect to the means of each column.

For instance, let's say I have 3 columns with 4 rows/values each:

1 6 2

1 2 3

2 7 5

2 8 4

and I would like to arrange the columns with respect to the means of the columns (i.e., 1.5 and 5.75 and 3.5, respectivly)

e.g. in an ascending order, that should result to the following new matrix:

1 2 6

1 3 2

2 5 7

2 4 8

Any recommendations on how to achieve this? Found various options for sorting, but so far didn't succeed in re-ordering according the the means.

Thanks a lot!

Stefan

Answer 1

[Scott MacKenzie]

Here's one way to do this:

M = [1 6 2;
    1 2 3;
    2 7 5;
    2 8 4]

[~, idx] = sort(mean(M));

M(:,idx) = M

Output:

M =

1 6 2

1 2 3

2 7 5

2 8 4

M =

1 2 6

1 3 2

2 5 7

2 4 8

[Stefan Schulreich]

Thanks, Scott! That helped a lot!

While this worked in this case, I noticed that for more or other arrangements of the columns, this worked in a slightly different way than intended. For instance, when the lowest mean was for the third column, the code then moved the content of the first column to the third, and so on ... but what I intended to do was the opposite: move the content of the third column (with the lowest mean) to the first column, then the content of the X column (second-lowest mean) to the second column, etc.

I found a workaround for this, by using the find command:

[~, idx] = sort(mean(M));

idx_new(1) = find(idx==1);

idx_new(2) = find(idx==2);

% ...and so on

M_sorted(:,idx_new) = M;

Best,

Stefan

[Scott MacKenzie]

Sorry, but I don't get your point. My code rearranges the columns so the column with the lowest mean becomes the 1st column, the column with the next lowest mean becomes the 2nd column, and so on. That's what is expected, if I understand correctly.

In the example matrix, the 1st column doesn't move because its mean is 1.5 which is the lowest of the three means. The 3rd column with a mean of 3.5 becomes the second column because it has the second lowest mean. The 2nd column with a mean of 5.75 has the highest mean and therefore becomes the 3rd column. Simple enough, or did I misunderstand in some way?

[Ernst Jan Hölscher]

Thanks Scott. This has been very helpful to me. I have however failed to implemnt this without that intermediate step. Wondering if there's a way to access that second column of sort() results within that last statement.

[Scott MacKenzie]

@Ernst Jan Hölscher, if you just want to access the 2nd column of the sort results, then use

M(:,idx(2))

after the 2nd statment in my solution, or

M(:,2)

after the 3rd statement.

Answer 2

[Image Analyst]

Scott's code has an error. It should be

M = M(:, idx);

not

M(:, idx) = M;

Here's a full demo:

m = randi(9, 4, 7)
meansOfColumns = mean(m, 1)
% Sort by the means
[sortedMeans, sortOrder] = sort(meansOfColumns)
m = m(:, sortOrder) % Correct.
% m(:, sortOrder) = m  % Not correct
% Verify by checking means again
meansOfColumns = mean(m, 1)

You'll see the columns are sorted in order of increasing column means. If you want to see Scott's way, comment out the "Correct" line and uncomment the "Not correct" line and you'll see the columns are not in order of increasing mean values.

[Scott MacKenzie]

@Image Analyst, ah, yes, right you are. The error doesn't appear in the 3-column example, but it's obvious enough with a larger data set. Thanks for the correction. And it only took 10 months! :) I guess we can thank @Ernst Jan Hölscher for bringing this question back to the fore. Perhaps @Stefan Schulreich will now accept the correct answer.