How can I extract a certain 'cluster' of elements according to a particular condition on the elements?
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I have a matrix (about 342 by 342) denoted by C(k,l) and I want to identify all cluster of indices of the original according to the condition C(k,l) > rho. I.e. I want all square matrices C'(a,b) of C(k,l) such that C'(a,b) > rho for all pairs of indices a and b
For example, if I have the matrix C(i,j) as:
C = 1 0.8 0.7
0.8 1 0.5
0.7 0.5 1
And rho = 0.6 then a correct square matrix I want my code to identify is:
C'= 1 0.7
0.7 1
This is not unique of course and the result as given by the example above is not necessarily a submatrix. I am not sure how/the best way to do this is in MATLAB? If possible, I would also like identify what a and b are for each possible matrix e.g. for my example above a and b can be 1 or 3. The matrices are always symmetric and the diagonal entries are always 1.
8 Kommentare
Antworten (2)
Kirby Fears
am 21 Jan. 2016
Bearbeitet: Kirby Fears
am 21 Jan. 2016
Assuming you only want to find submatrices along the diagonal of C, the following code extracts all square submatrices (>rho) into a table S. This should be a good starting point for whatever assumptions you end up deciding on.
% make data
sizeC = 342;
rho = 0.6;
c = rand(sizeC);
c(1:(sizeC+1):end) = 1;
% prep
S = cell((sizeC-2)*(sizeC-1),3);
varNames = {'S','sizeS','diagC'};
idxRho = c>rho;
counterS = 1;
% traverse submatrix size
for sizeS = (sizeC-1):-1:2,
% traverse diagonal of c
for d = 1:(sizeC-sizeS),
% store valid submatrix with meta info
if all(idxRho(d:(d+sizeS-1),d:(d+sizeS-1))),
S(counterS,:) = {c(d:(d+sizeS-1),d:(d+sizeS-1)),...
sizeS,d};
counterS = counterS + 1;
end
end
end
% drop extra rows of S
if counterS<=size(S,1),
S(counterS:end,:)=[];
end
% convert S to table
S = array2table(S,'VariableNames',varNames);
Hope this helps.
9 Kommentare
Stephen23
am 23 Jan. 2016
Bearbeitet: Stephen23
am 24 Jan. 2016
Assuming that the input matrix is always square and symmetric:
>> D = [1,0.8,0.9,0.5;0.8,1,0.6,0.1;0.9,0.6,1,0.7;0.5,0.1,0.7,1]
D =
1 0.8 0.9 0.5
0.8 1 0.6 0.1
0.9 0.6 1 0.7
0.5 0.1 0.7 1
>> rho = 0.6;
>> [R,C] = find(tril(D,-1)>rho);
>> out = arrayfun(@(r,c)D([r,c],[r,c]),R,C,'UniformOutput',false);
>> out{:}
ans =
1 0.8
0.8 1
ans =
1 0.9
0.9 1
ans =
1 0.7
0.7 1
5 Kommentare
Stephen23
am 27 Jan. 2016
This task might not be solvable using a standard PC: there are potentially a lot of such matrices:
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