What is the difference between soft and hard expectation maximization?

EDIT: ok, i've found out this paper: http://ttic.uchicago.edu/~dmcallester/ttic101-07/lectures/em/em.pdf that explain quite well the situations

  • $\begingroup$ You may need to explain what you mean by soft and hard EM, or provide a link. $\endgroup$ Nov 19, 2010 at 11:02

2 Answers 2


Based on the paper you linked to, I would argue that the term EM usually refers to the "soft" version. The key distinction seems to be that instead of taking an expectation in the E-step, the "hard" version finds a mode.

A good explanation of the distinction is available in chapters 20-22 of David Mackay's book (which is available online).


I suggest you look at this: http://cogcomp.cs.illinois.edu/papers/SamdaniChRo12.pdf

There is a nice comparison in table 1.


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