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I have just started reading about Latent Dirichlet Allocation LDA and want to apply it to my project.

May I know if LDA is able to assign a topic to more than one word?

For example, Article A talks about "river banks" while Article B talks about "The role of banks in finance". Hence, will LDA allow the word "banks" to potentially be assigned to two different topics?

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Briefly, my answer is "yes".

The result of any LDA inference algorithm is $\theta_{d,t}$ and $\phi_{t,w}$, distribution of topics in each document and distribution of terms in each topics. Given these distributions, one can obtain estimate for $p(z|d,w)$, conditional probability of a topic $z$ for word $w$ in document $d$: $$ p(z|d,w)=\frac{p(z,d,w)}{\sum\limits_{s=1}^K p(s,d,w)}=\frac{\theta_{d,z} \phi_{z,w}}{\sum\limits_{s=1}^{K} \theta_{d, s} \phi_{s, w}} $$ Further utilizing of this information can be, for example, assigning the single most probable topic for a word. But it's not obligatory.

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