largest uncorrelated set in a correlation matrix

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sanpal82 2014-8-11

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https://ww2.mathworks.cn/matlabcentral/answers/147190-largest-uncorrelated-set-in-a-correlation-matrix

I have a large correlation matrix (1000x1000) and I want to find the largest uncorrelated set(s) from the matrix. The matrix contains only ones and zeros, and all the diagonal elements are ones, since this is a correlation matrix. The matrix is also symmetric.

I have provided an example correlation matrix for illustration (A to W) and the intended output matrix (X's).

So far my approach, which doesn't scale well for large correlation matrices:

1) Start with A and loop through A to W and find all the uncorrelated 2x2 sets.

2) Repeat step one now starting with B and loop through A to W, and so on...

3) With steps 1&2, I have all the 2x2 uncorrelated sets.

4) Now for each 2x2 uncorrelated set, loop though A to W again and find the 3x3 uncorrelated sets.

5) For each uncorrelated 3x3 set, loop though A to W to find the 4x4 uncorrelated sets.

6) Repeat this process till you find the largest uncorrelated set(s) -- X1, X2, X3,...

Obviously, this is a brute force approach, and doesn't scale well with higher dimension matrices. I would appreciate it if anyone could point me in the right direction to solve this problem efficiently in MATLAB.