# How to use ICA as a specific factor rotation in orthogonal factor model

I am trying to understand the way ICA is used as factor rotation in the traditional orthogonal factor model. The idea of using ICA as a specific factor rotation is often mentioned in the literature (ex. Independent component analysis by Hyvärinen, Karjunen, Oja), but it is not really explained.

I found this one paper "The independent factor analysis approach to latent variable modeling" by Montanari and Viroli, and based on it my understanding is as follows:

Assume an orthogonal factor model $$X = L F + \epsilon$$, with the usual assumptions.

First, we estimate the loadings $$L_r$$ and factors (scores) $$F_r$$ up to a rotation, for example by using PCA and least squares.

After this, we consider the ICA model according to which $$F_r = AF$$, where the factor $$F$$ represents the independent sources. Now by estimating the above ICA model we get the "independent factors" as $$F = A^{-1}F_r$$.

Now my question has two parts: (1) How do I obtain from this the actual loadings $$L$$ of the factor model? (2) Is my overall understanding of the process correct? And generally, if there is something that I have misunderstood, or if you know there is a better approach to this problem please let me know.

Thanks for the help, really appreciate it :)