  The question of how to determine the number of independent latent factors
(topics) in mixture models such as Latent Dirichlet Allocation (LDA) is of
great practical importance. In most applications, the exact number of topics is
unknown, and depends on the application and the size of the data set. Bayesian
nonparametric methods can avoid the problem of topic number selection, but they
can be impracticably slow for large sample sizes and are subject to local
optima. We develop a guaranteed procedure for topic number recovery that does
not necessitate learning the model's latent parameters beforehand. Our
procedure relies on adapting results from random matrix theory. Performance of
our topic number recovery procedure is superior to hLDA, a nonparametric
method. We also discuss some implications of our results on the sample
complexity and accuracy of popular spectral learning algorithms for LDA. Our
results and procedure can be extended to spectral learning algorithms for other
exchangeable mixture models as well as Hidden Markov Models.
