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I'm doing uniqueness on factor loading matrix in a factor model.

$ y = \Lambda f + \epsilon$

where $ f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega) $ and $\epsilon \perp f$.

It's well known that factor loading matrix $\Lambda$ is not identifiable.

My goal is to use a prior on $\Lambda$ such that it can be identified.

I know that there are many papers which have already work into this problem, but they are under the framework which assume $\Sigma$ and $\Omega$ are diagonal matrix.

However, I want to do that under the situation that $\Sigma$ and $\Omega$ are not diagonal matrix.

Has it already have paper on this part? Or is there any idea that I can achieve this?

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