Goodness of fit metric to compare topic models NMF vs LDA Does anyone have a good idea for how to compare topic modeling done by NMF and LDA? Let's say I fit LDA to a dataset and generate topic-word and document-topic distributions--I can use perplexity, for instance, to measure the goodness of fit of the model. If I fit NMF to the same dataset and generate topic-word and document-topic distributions, I can take the resultant fitted data as $X^{Est} = HW^T$ and use $\|X^{Original} - X^{Est}\|_{Fro}$ as a goodness of fit of the model.

What is an objective metric that I can use to compare the goodness of fits to each other? Can either of these metrics be used for the other model?
NMF and LDA models produce topic-word and document-topic distributions, so you can compare these models on evaluation tasks of topic coherence (i.e. evaluating topic-word distributions), document clustering/classification (i.e. evaluating document-topic distributions) or information retrieval (i.e. evaluating topic-word and document-topic distributions together). 

See some examples in "Improving topic models with latent feature word representations", "LDA-Based Document Models for Ad-hoc Retrieval".