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By Andrew Ng's lecture notes (which you can find at http://cs229.stanford.edu/notes2020spring/cs229-notes9.pdf), the factor analysis model has the following structure:

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Written out mathematically like this, it's quite obvious that we are trying to estimate the density function of random variable $x$.

However, I find it difficult to connect the math (especially the matrices $\mu$, $\Lambda$ and $\Phi$) with how factor analysis is used in practice to discover "important latent variables". Can someone elaborate this connection a bit more? In particular, what further analysis do we perform with these matrices?

Wiza
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  • Hi, Wiza. On this site, you will find a gerat number of threads on Factor analysis (check tag 'factor-analysis'). Please read them. If you have specific question after that, ask it. Now about your citation and the question. If you are adopting a "data analyst" attitude (asking about "important latent variables") rather than a "mathematical statistics" attitude, then starting to study FA from "estimate the density function of random variable" is not the best decision. – ttnphns Nov 24 '20 at 14:15
  • There are many approaches to dimension reduction, i.e., taking a large, even massive, number of features and expressing them in a much lower dimensional form. This is desirable as it makes subsequent analyses more tractable. Factor analysis, in its classic form, creates linear combinations of correlated inputs, kind of like running a regression without a target variable, where the resulting eigenvalues and eigenvectors summarize the redundancy in the input data. –  Nov 24 '20 at 14:16
  • Start with https://stats.stackexchange.com/q/1576/3277. Pay attention there to my answer https://stats.stackexchange.com/a/288646/3277 which is detailed enough. You must know PCA well before you turn to FA. – ttnphns Nov 24 '20 at 14:16

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