  This paper proposes a new methodology to study sequential corpora by
implementing a two-stage algorithm that learns time-based topics with respect
to a scale of document positions and introduces the concept of Topic Scaling
which ranks learned topics within the same document scale. The first stage
ranks documents using Wordfish, a Poisson-based document scaling method, to
estimate document positions that serve, in the second stage, as a dependent
variable to learn relevant topics via a supervised Latent Dirichlet Allocation.
This novelty brings two innovations in text mining as it explains document
positions, whose scale is a latent variable, and ranks the inferred topics on
the document scale to match their occurrences within the corpus and track their
evolution. Tested on the U.S. State Of The Union two-party addresses, this
inductive approach reveals that each party dominates one end of the learned
scale with interchangeable transitions that follow the parties' term of office.
Besides a demonstrated high accuracy in predicting in-sample documents'
positions from topic scores, this method reveals further hidden topics that
differentiate similar documents by increasing the number of learned topics to
unfold potential nested hierarchical topic structures. Compared to other
popular topic models, Topic Scaling learns topics with respect to document
similarities without specifying a time frequency to learn topic evolution, thus
capturing broader topic patterns than dynamic topic models and yielding more
interpretable outputs than a plain latent Dirichlet allocation.
