Find minimum in groups defined by cell arrays

I have a cell array I and a vector X. Each item in I specifies a group of indices of items in X. I would like to find the minimum in each group.

The naive code which does the work is

M = zeros(size(I))
for i = 1:numel(I)
    M(i) = min(X(I{i}));
end

Or alternatively

M = cellfun(@(idx) min(X(idx)), I);

Both approaches are not as fast as I would like. Is there any way to make it faster? For example, transform the input, somehow, into a valid input of `splitapply' or something similar?

[Akira Agata]

Questions for clarification:

(1) I think your cell array I and vector X looks like:

X = rand(4,1);
I = {[true;true;false;false],[false;false;true;true]};

Is my above understainding correct?

(2) Does each item in X belongs to only one group? or sometimes belongs to multiple groups like following?

X = rand(4,1);
I = {[true;true;true;false],[false;false;true;true]}; % 3rd item belongs to both group

[Matt J]

You had to have used a for-loop just to create I. Are you sure that's not going to bottleneck your code even if you did manage to accelerate the min operations?

[Alexander Shtof]

I contains indices (integers) and not logical vectors. Becides, the assumptions are correct.

Answer 1

[Matt J]

Cell arrays aren't built for speed. Instead of keeping I as a cell array, therefore, it would be better to encode the same information in the columns of a sparse binary matrix,

 for i=1:N
  I{i}=indices(:).'; %computed somehow   
  J{i}=ones(1,numel(indices));
 end
 S=sparse([I{:}],[J{:}],true,numel(X), numel(I));

Now, you can do your computation as follows,

xmax=max(X(:));
M = xmax - max((xmax-X(:)).*S,[],1);

[Alexander Shtof]

I cannot change the structure of I, since it is obtained from another MATLAB function which I cannot control - the `rangesearch' function.

[Matt J]

Well, you can still derive the sparse matrix, S, from I as above and do the min. computations as shown. If you are going to do multiple computations like this, then it may prove worth the investment to build S.

[Image Analyst]

Like Matt said, I bet it's that you are using cell arrays, not that you're using a for loop. For loops are fast now. I just did a for loop (doing nothing inside) of one hundred million iterations and it took 0.09 seconds. I don't know how many iterations you're doing or what kind of speed/times you're getting but I'm pretty sure it's not the for loop itself causing a slow program. I bet it's the cell array. But even cell arrays are not that slow unless there are lots of cells, like tens of thousands, not a few dozen. What times are you seeing?