Data preprocessing

Question

How would you preprocess 2 dimensional data to have 0 mean? Say you have a matrix $M $ that is $p \times q $. Would you calculate the mean of each row, get a vector of length $q $ and subtract each element of the vector from the corresponding column?

Answer 1

If your data are 2-dimensional, then the matrix $M$ would have the size $p \times 2$ or $2 \times p$. In either case, you need to take the mean along the $p$ dimension. This will give you a 2-element mean vector $m$. Then you have to subtract it from every row (or column) of $M$.

Answer 2

Let $M$ be of size $p \times q$, as stated in your question. If you want the mean of the entire array to be zero:

M = M - mean(M(:));

If you want each column individually to have zero mean:

M = M - repmat(mean(M,1), p, 1);

If you want each row individually to have zero mean:

M = M - repmat(mean(M,2), 1, q);