Ordinarily, this factorization is NP-Hard (Arora et al., 2012).
given a set of anchor words, or words which uniquely identify a topic, the computation requires only O(KV 2 + K 2 V I) where K is the number of topics, V is the size of the vocabulary, and I (typically around 100) is the average number of iterations (Arora et al., 2013).