Multiscale analysis of count data through topic alignment

Topic modeling is a popular method used to describe biological count data. With topic models, the user must specify the number of topics K. Since there is no definitive way to choose K and since a true value might not exist, we develop a method, which we call topic alignment, to study the relationships across models with different K. In addition, we present three diagnostics based on the alignment. These techniques can show how many topics are consistently present across different models, if a topic is only transiently present, or if a topic splits into more topics when K increases. This strategy gives more insight into the process of generating the data than choosing a single value of K would. We design a visual representation of these cross-model relationships, show the effectiveness of these tools for interpreting the topics on simulated and real data, and release an accompanying R package, alto.