Alexander Ihler, Padhraic Smyth
Data sets that characterize human activity over time through collections of timestamped events or counts are of increasing interest in application areas as humancomputer interaction, video surveillance, and Web data analysis. We propose a non-parametric Bayesian framework for modeling collections of such data. In particular, we use a Dirichlet process framework for learning a set of intensity functions corresponding to different categories, which form a basis set for representing individual time-periods (e.g., several days) depending on which categories the time-periods are assigned to. This allows the model to learn in a data-driven fashion what "factors" are generating the observations on a particular day, including (for example) weekday versus weekend effects or day-specific effects corresponding to unique (single-day) occurrences of unusual behavior, sharing information where appropriate to obtain improved estimates of the behavior associated with each category. Applications to realworld data sets of count data involving both vehicles and people are used to illustrate the technique.