Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm working with this model:

  • A fixed and finite set of documents: $D = \lbrace d_1, d_2, \dots, d_D\rbrace$
  • A fixed and finite set of terms that can appear in the documents: $V = \lbrace v_1, v_2, \dots, v_V\rbrace$
  • A fixed and finite set of latent classes: $T = \lbrace t_1, t_2, \dots, t_T\rbrace$
  • A probability distribution over the latent classes: $P(t)$
  • For each latent class, a distribution over terms: $P(\textbf{v}|t)$
  • For each latent class, a distribution over documents: $P(\textbf{d}|t)$

Given a corpora of documents and chosen the probability distribution, the likelihood of the model is: $$L = \prod_d \prod_v [P(d,v)]^{n(d,v)}$$ where n(d,v) is the number of occurences of the term $v$ in the document $d$, and: $$P(d,v) = \sum_t P(t)P(v|t)P(d|t)$$

It's know as aspect model of the Probability Latent Semantica Analysis.

I would like to know if it is possible to estimate the number of optima of the likelihood function, or if we can say something else about it.

Thank you.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.