with '<math>c'</math> being the words' topic. Note that the number of topics is a hyperparameter that must be chosen in advance and is not estimated from the data. The first formulation is the ''symmetric'' formulation, where <math>w</math> and <math>d</math> are both generated from the latent class <math>c</math> in similar ways (using the conditional probabilities <math>P(d|c)</math> and <math>P(w|c)</math>), whereas the second formulation is the ''asymmetric'' formulation, where, for each document <math>d</math>, a latent class is chosen conditionally to the document according to <math>P(c|d)</math>, and a word is then generated from that class according to <math>P(w|c)</math>. Although we have used words and documents in this example, the co-occurrence of any couple of discrete variables may be modelled in exactly the same way.
So, the number of parameters is equal to <math>cd + wc</math>. The number of parameters grows linearly with the number of documents. In addition, although PLSA is a generative model of the documents in the collection it is estimated on, it is not a generative model of new documents.
