Modeling adoptions and the stages of the diffusion of innovations

Understanding the dynamics underlying the diffusion of new ideas or technology in a society is an important task with implications for sciences such sociology and economics, as well as important business applications, especially in marketing. In this article, we take a first step in this direction, by studying the problem of how to model, in a simple and useful abstraction, the complex process of innovation diffusion. Our unique input is a database of adoptions $$\mathbb {D}$$D, which is a relation (User,Item,Time) where a tuple $${\left\langle u, i, t\right\rangle } \in \mathbb {D}$$u,i,t∈D indicates that the user u adopted the item i at time t. For our aim, we propose a stochastic model which decomposes a diffusion trace (i.e., the sequence of adoptions of the same item i) 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 datasets 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.