Randomise List with Repetitions

I managed to create a list of images (images, 80% one image; 20% another one). These images are to be randomized, which is fine, except for the fact that:

• I need there to be at least one of the "20% Images" in every 12 rows,
• There can be no more than 3 "20% Images" in every 12 rows.

Im able to randomize the list however can't figure out how to set these randomization restrictions I want. This is for an oddball experiment. Any help is appreciated.

Answer 1

[Star Strider]

One approach:

Ncols = 10;                                     % Columns In Matrix
v = 8*ones(12,Ncols);                           % Preallocate
p20 = randi(3, 1, Ncols);                       % Number Of Rows Allocated To ‘20%’ In Each Column
for k1 = 1:Ncols
    idxv = randperm(12,p20(k1));                % Choose Rows For ‘20%’
    v(idxv,k1) = 2;                             % Define Matrix
end

v =
     8     2     8     2     8     8     8     2     8     8
     2     8     8     8     2     8     8     2     8     8
     8     2     8     8     2     8     2     8     8     8
     2     8     2     8     2     8     8     8     8     8
     8     8     8     8     8     2     8     8     8     8
     8     8     8     8     8     8     8     8     8     8
     8     8     8     8     8     8     8     8     2     2
     2     8     8     2     8     8     2     8     8     2
     8     8     8     8     8     8     8     8     2     8
     8     8     8     2     8     8     8     8     2     8
     8     8     8     8     8     8     8     8     8     8
     8     8     2     8     8     8     8     8     8     8

The ‘80%’ images are any corresponding to an ‘8’, and the ‘20%’ to a 2.

[Tutasaurus]

Hmmm not sure this would work. My list consists of three coloumns in a cell matrix.

• Coloumn one has the specific image name (e.g. image1.bmp)
• Coloumn two has the a number (1-3) indicating the image where 3 is the 80% image
• Coloumn three can be ignored, its a coloumn of all ones.

[Star Strider]

My code does what you originally requested. It would work with ‘Column two’ if you replace the ‘8’ values with ‘3’, and the ‘2’ values with whatever designates the 20% image(s).

[Tutasaurus]

Ok thanks! I think I can use this and append the file names depending on whether its an "8" or "2" in a loop as well. Will give it a try.

[Star Strider]

My pleasure!

Answer 2

[Roger Stafford]

Without your restriction as to the number of 20% images, you would be asking for a binary distribution for each set of 12 images. In that distribution the probabilities for the three cases you are restricted to are:

p1 = 12/1*.2*.8^11             % <-- One 20% case
p2 = 12*11/1/2*.2^2*.8^10      % <-- Two 20% cases
p3 = 12*11*10/1/2/3*.2^3*.8^9  % <-- Three 20% cases

Given your restriction, these normalize so as to add to one by doing this:

s = p1+p2+p3
p1 = p1/s
p2 = p2/s
p3 = p3/s

These latter are respectively about 28%, 39%, and 33%. The only way Star’s method deviates from this is that he assigned equal probabilities for these three cases in his code. If you want a more accurate realization as a “restricted” binary distribution, you would have to replace the

p20 = randi(3, 1, Ncols);

step in Star’s code with

r = rand(1,Ncols);
p20 = sum([(p1<=r);(p1+p2<=r)],1)+1;

where the above normalized p1 and p2 are used. The number p20 is still either 1, 2, or 3 but with probabilities p1, p2, and p3 respectively, instead of being equal.