How to loop in a single line for the given statement

Suppose i have a n * d matrix (2D datas) . Here n=2 , so i have been able to give 2 statements inside for loop to calculate the mean normalization. But if n would have been higher, then the number of statements inside for loop would increase. Is there a way i can write it in a single line.

function meannormalize
F = [1 1;1 1.5;1.5 1.5;5 5;5 5.5;5.5 5;6 5;10 7;10.5 6;9 7;10 8]';
[n dim]=size(F);
MEAN=mean(F,2)
for i=1:dim
    F(1,i)=(F(1,i)-MEAN(1))/norm(F(1,i)-MEAN(1));
    F(2,i)=(F(2,i)-MEAN(2))/norm(F(2,i)-MEAN(2));

end
end

[OCDER]

Just making sure there's no math error. Is this the result you really want?

F = 
  -1    -1    -1    -1    -1    -1     1     1     1     1     1
  -1    -1    -1     1     1     1     1     1     1     1     1

[HIRAKJYOTI BASUMATARY]

No it returns

-1  -1  -1  -1  -1  -1  1  1  1  1  1
-1  -1  -1  1  1  1  1  1  1  1  1

[Jan]

@HIRAKJYOTI: It would be much easier to see the difference, if you use the same formatting as Donald.

[HIRAKJYOTI BASUMATARY]

@Donald: I am trying spherical k - means clustering .. So i have to mean normalize the datas. So i think this is the way. I am also not sure.

[Cam Salzberger]

If you are looking to normalize the data, you probably want norm(F-MEAN), as shown in my answer, as opposed to doing element-wise "normalization".

If you've got R2016a or before, you can do it with:

normVal = norm(F-repmat(MEAN, 1, size(F, 2)));

and then just divide that every loop, or in vectorized format.

[OCDER]

Not familiar with k-means clustering, but are there 2 different "norm"? It seems you want to "Normalize" vectors in dimension D (row-wise) with respect to the "Euclidean norm" of that dimension's mean value, like this?

MEAN = mean(F, 2);
NORM = zeros(size(F));
for k = 1:size(F, 1)
    NORM(k, :) = (F(k,:) - MEAN(k)) / norm(F(k,:) - MEAN(k));
end

NORM = 
 -0.4209   -0.4209   -0.3776   -0.0747   -0.0747   -0.0315    0.0118    0.3579    0.4012    0.2714    0.3579
 -0.4946   -0.4291   -0.4291    0.0298    0.0953    0.0298    0.0298    0.2920    0.1609    0.2920    0.4231

Also, Matlab does have kmeans clustering function too, though not sure if it does what you want.

Answer 1

[Cam Salzberger]

The norm of a scalar is just going to be the absolute value, so that can be easily removed. Then you're doing basically (a - b)/abs(a - b). Which is just sign(a - b).

This works in R2016b+ due to implicit expansion:

sign(F-MEAN)

Otherwise, you can get fancy with repmat:

sign(F-repmat(MEAN, 1, size(F,2)))

For your future use, here's how you could do a double loop:

for jj = 1:dim
    for ii = 1:n
        F(ii, jj) = (F(ii, jj)-MEAN(ii))/norm(F(ii, jj)-MEAN(ii));
    end
end

But it's easier to just vectorize the whole thing (R2016b+):

F = (F-MEAN)./norm(F-MEAN);

This will be a different result since the norm will actually be a scalar value (since it's taking the norm of the whole matrix. Not sure if that's what you really wanted. If not, you can take the "norm" of each scalar with just:

F = (F-MEAN)./abs(F-MEAN);

-Cam

[HIRAKJYOTI BASUMATARY]

Thank you very much sir. I will definitely keep this technique in mind