Consider a binary matrix:
$$\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 &1 \\ \vdots & \vdots &\vdots \\ 1 & 1 & -1\end{pmatrix}$$
with a random distribution of 1 and -1 scattered throughout the matrix. Say that we need to add another column vector made also made of -1's and +1's to this matrix with:
- Roughly the same number of 1's and -1's
- As incorrelated as possible with any other column (i.e. Pearson correlation of the new column with any other column as close to 0 as possible)
There could certainly be multiple solutions to this problem. Does this problem have a name? Any known family of algorithms or heuristics to solve it?
