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Topic models is a probabilistic approach to Document Clustering:

- create a probabilistic generative model for text documents
- represent corpus as a function of hidden variables

Notation and problem:

- $D_1, \ ... \ , D_n$ are documents
- $T_1, \ ... \ , T_k$ are topics (sort of "clusters")
- each document may belong to several topics - so these "clusters" are Fuzzy
- probability of $D_i$ belonging to $T_j$ is $P(T_j \mid D_i)$
- but cluster membership is secondary in this problem
- the main problem is to find latent topics that generated documents - which is why it's called Topic Modeling
- let $t_1, \ ... \ , t_d$ be $d$ terms from the lexicon
- then the probability that $t_l$ occurs in $T_j$ is $P(t_l \mid T_j)$

Thus, we need to estimate the following probabilities:

- $P(T_j \mid D_i)$ and $P(t_l \mid T_j)$
- usually parameters are learned via maximum likelihood methods like Expectation Maximization

There are two types of Topic Modeling techniques:

- Aggarwal, Charu C., and ChengXiang Zhai. "A survey of text clustering algorithms." Mining Text Data. Springer US, 2012. [1]