Parameters

• $K$: number of topics
• $M$: number of documents
• $N_m$: length of m-th document
• $V$: size of vocabulary
• $\varphi$: $K\times V$, word distribution of topics
• $\theta$: $M\times K$, topic distribution of documents

Likelyhood Function

$$\log p(C) = \sum_{d\in C} \log p(d)$$
where
$$\log p(d) = \sum_{w\in V} c(w,d)\log p_d(w)$$
$$p_d(w)=\sum_{k=1}^K \theta_{d,k}p(w|\varphi_k)$$
ML is done by EM algorithm

Criticism

• number of parameters: MK+KV, grows linearly by the number of documents. So pLSA is prone to overfitting and can't easily handle unseen documents (But sometimes what we want is just to "overfit" our dataset)

Reference

Text Mining: https://www.coursera.org/learn/text-mining