evolutions of topic models for modling document and image

I summarized the evolutions of the topic models for modeling documents and images using the above figure. Here are the notations:

• NB-BoW: Naive Bayes bag of words, i.e., mixture of unigram
• pLSA: probabilistic latent semantic analysis
• LDA: latent Dirichlet allocation
  
• FMM: finite mixture model
• FHMM: finite hierarchical mixture model
• DPMM: Dirichlet mixture model
• HDP: hierarchical Dirichlet process mixture model

The texts on the arrows mean the changes that need to be done to evolve from one model to the other:

• w-> x denotes to generalize the word x from a categorical variable to a
  real variable, x, that can be either discrete or continuous
• hierarcy denotes to add a hierarchy to the original model
• K topics denotes to extend from one topic per document to multiple topics
• K -> \infty denotes to derive an infinite limit of the original model.

This is not a complete summary. For example, HMM is not included.

Some interesting observations: there are three paths to evolve a NB-BoW model to a
HDP-MM model, which we always need to perform all the above four extensions
no matter which path we choose.