how to determine the number of topics for LDA?

I am a freshman in LDA and I want to use it in my work. However, some problems appear.

In order to get the best performance, I want to estimate the best topic number. After reading "Finding Scientific topics", I know that I can calculate logP(w|z) firstly and then use the harmonic mean of a series of P(w|z) to estimate P(w|T).

My question is what does the "a series of" mean?

Unfortunately, there is no hard science yielding the correct answer to your question. To the best of my knowledge, hierarchical dirichlet process (HDP) is quite possibly the best way to arrive at the optimal number of topics.

If you are looking for deeper analyses, this paper on HDP reports the advantages of HDP in determining the number of groups.

A reliable way is to compute the topic coherence for different number of topics and choose the model that gives the highest topic coherence. But sometimes, the highest may not always fit the bill.

See this topic modeling example.