Does EM-algorithm only work with missing data? If not, what is the idea to assume that we have missing data?

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    Any density that can write as$$f_\theta(x)=\int_\mathscr{Y} g_\theta(x,y)\text{d}y$$qualifies for EM, not truly a restriction. Provided you can implement the E step. – Xi'an Sep 21 '16 at 8:31
  • Check also:… – Tim Sep 21 '16 at 8:42
up vote 5 down vote accepted

I think the Wikipedia for EM algorithm has everything you want and it probably explains better than I do. You can also use the EM algorithm for latent variables; no missing data but variables that you can't observe and measure. The idea of the algorithm is to iteratively adjust your missing data/latent variables until your maximum likelihood estimate converges.

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