# pLSA using tempered EM

In an article by Hofmann pdf, he proposes:

initialize $β$ to one, run until convergence, then rescale $β$ by a factor $η<1$, run again until convergence, and iterate this until changing $β$ no longer improves the result.

I used the TEM algorithm on a dataset for my project, but the problem is that the algorithm ends up traped in several local minima and doesn't give me full convergence. My question is: what is the optimal condition under which I can assume that the algorithm converged?

If you are converging to a local minima instead of the global minima, there may be a problem with the values used for $β$ or $η$. You may try initializing $β$ to a different value, or using a larger scaling factor $η$ (closer to one).