0
$\begingroup$

Problem

I have $J$ matrices $C_{j}$, which are $K \times M$.

Elements of each matrix $C_{j}$ are between 0 and 1.

I want to randomly choose $J$ matrices $A_{j}$ and one matrix $B$ such that:

  • Elements of all matrices $A_{j}$ and matrix $B$ are between 0 and 1
  • $A_{j}B = C_{j}$ for all $j$.
  • Dimensions of each matrix $A_{j}$ is $K \times L$
  • Dimensions of matrix $B$ is $L \times M$
  • $L \lt M \lt\lt J$
  • $J$ is ~50,000. $K$, $L$, and $M$ are ~15.

Attempt

I thought about the following:

  1. Randomly choose a matrix $B$ within bounds.
  2. Fix $B$ and find least square solutions $A_{j}$ such that $A_{j}B \approx C_{j}$
  3. Replace any element in $A_{j}$ that is not between 0 and 1 by a random value between 0 and 1.
  4. Fix $A_{j}$ and find least square solution $B$ such that that $A_{j}B \approx C_{j}$
  5. Replace any element in $B$ that is not between 0 and 1 by a random value between 0 and 1.
  6. Repeat steps 2 to 6 till converge.

Since $J$ is large, this might take a long time.

Question

What is the standard way to do this?

Thank you.

$\endgroup$
  • $\begingroup$ Please credit the original source of the problem in the question. $\endgroup$ – Apass.Jack Dec 16 '18 at 16:16
  • $\begingroup$ @Apass.Jack Where did you see this problem? What is the "original source"? $\endgroup$ – R zu Dec 16 '18 at 16:21
  • $\begingroup$ The issue is not about whether I have seen this problem. The issue is, is this problem created by you? If yes, it is better stated that way. If not, then it is a general practice that the original copyright owner be credited, unless it is in public domain. Or something like that. $\endgroup$ – Apass.Jack Dec 16 '18 at 16:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.