0

I'm wondering if anybody knows about the structure of $A^{m\times n}$ in real big data LASSO problems. I want to ask if anybody know what is the degree of sparsity and separability(number of nonzero elements in each row) of this kind of problem in various fields. I suspect that this kind of structure exists in reality (few number of nonzero in each row and columns). My question also extends to how dense $A$ can be. I'm asking this because I saw many assumptions which are presumed by authors of some strong algorithms for solving this problem.

Please provide me with an answer.

Amir D.
  • 1

1 Answers1

0

Not Sure if this answers your question:

If you are asking about "Sparse sensing (or measurement) Matrices", the answer is Yes, there are sparse measurement matrices in reality. Devore's scheme of a deterministic sensing matrix is an example, in which every column contains $\ p^2$ elements where only $p$ of them are nonzero. ( $p$ is a power of a prime number )

About your second question: It's not clear what you mean by dense. A measurement matrix can be an ${m\times} n$ Gaussian matrix which is not sparse at all or it can be a sparse matrix (like the one I mentioned) which is not dense at all.

I hope that helps.

Mahdi
  • 36