# How does LDA (Latent Dirichlet Allocation) assign a topic-distribution to a new document?

I am new to topic modeling and read about LDA and NMF (Non-negative Matrix Factorization). I understand the training process work. Let's say I have 100 documents and I want to train an LDA for these documents with 10 topics. However, I don't really understand how does this model assign topic to an unseen document?

I used Gensim. After training, I have an LDA trained model and a dictionary with most frequent words. Let's say, I have an unseen new document with the following text:

This is just a test text about topic modeling and LDA.


Can someone explain step by step how a topic distribution is assigned to this new document in terms of algorithmic steps? The same goes for NMF method.

• By the context, I understand that LDA refers to Latent Dirichlet Allocation, but please clarify this in the question. Also include the full name for Non-negative Matrix Factorization. Jan 29, 2018 at 14:37
• The Bayes decision rule of assigning topics to new documents depends on the loss function. Jan 29, 2018 at 14:49
• LDA does not assign topics to documents, it assigns topics to words and topic-distributions to documents.
– guy
Jan 29, 2018 at 15:23
• @guy I should have explicitly specified that. I meant topic distribution. Jan 29, 2018 at 15:25
• The topic distribution represented as a point on the $n_{topic}$-dimensional simplex, and is inferred by looking at the posterior under a Dirichlet prior. If we were to use, say, a Gibbs sampler, the topic distribution would be updated across iterations by sampling from the associated full conditional, which by conjugacy is another Dirichlet.
– guy
Jan 29, 2018 at 17:23