How to use QR-Decomposition to reduce the dimension of a dataset?

Question

Let A be a matrix of dimension m×n, representing the original data set.

The QR decomposition, [Q, R] = qr (A) produces:

• Upper triangular matrix R of the same dimension as A

• Unitary matrix Q

so that A = Q*R

If [m, n] = size (A), then

Q is m-by-m and

R is m-by-n

How can I use QR-Decomposition to reduce the dimension (reduce the number of columns or features) of A?

Answer 1

Generally, for rank reduction you should prefer to use the singular value decomposition unless you know that the original matrix is indeed rank deficient. This is because the svd orders the singular values, whereas the QR decomposition does not.

Nonetheless, I would suggest you try a simple example. If a matrix A is mxn with a rank of p