Modeling Adoptions and the Stages of the Diffusion of Innovations

We study the data mining problem of modeling adoptions and the stages of the diffusion of an innovation. For our aim we propose a stochastic model which decomposes a diffusion trace (sequence of adoptions) in an ordered sequence of stages, where each stage is intuitively built around two dimensions: users and relative speed at which adoptions happen. Each stage is characterized by a specific rate of adoption and it involves different users to different extent, while the sequentiality in the diffusion is guaranteed by constraining the transition probabilities among stages. An empirical evaluation on synthetic and real-world adoption logs shows the effectiveness of the proposed framework in summarizing the adoption process, enabling several analysis tasks such as the identification of adopter categories, clustering and characterization of diffusion traces, and prediction of which users will adopt an item in the next future.