Consider applying PLSI to the following corpus $($each line is a separate document$)$:

BACCA

CAABBBA

ACBBABAB

furthermore, assume that there are two topics, and A$,$B$,$C are the only types that are available.

a$.$ Now suppose we initially assigned words to topics as above $($black for topic $1,$

red$/$underline for topic $2).$ Calculate the topic$-$word vectors and document$-$topic vectors.

b$.$ Use the vectors generated in part $($a$)$ to calculate the topic probability for each word in

the corpus

c$.$ Use the result of $($b$)$ to recalculate the topic$-$word vectors and document$-$topic vectors.

d$.$ Calculate whether the vectors in $($c$)$ is better for the set of documents.