# 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?

• Thanks for the cursory - but useful - connection of topic coherence to topic-word, doc clustering/classification to evaluation of doc-topic and IR to evaluation of topic-word and doc-topic together. I had not seen that presented before. – javadba Dec 14 '17 at 16:36