We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a ‘long tail’ where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product, and pricing categories for which viral marketing seems to be very effective.
There are numerous other models of influence spread in social networks. One of the first and most influential diffusion models was proposed by Bass @cite_5 . The model of product diffusion predicts the number of people who will adopt an innovation over time. It does not explicitly account for the structure of the social network but it rather assumes that the rate of adoption is a function of the current proportion of the population who have already adopted (purchased a product in our case). The diffusion equation models the cumulative proportion of adopters in the population as a function of the intrinsic adoption rate, and a measure of social contagion. The model describes an S-shaped curve, where adoption is slow at first, takes off exponentially and flattens at the end. It can effectively model word-of-mouth product diffusion at the aggregate level, but not at the level of an individual person, which is one of the topics we explore in this paper.
@cite_5
2206697650 2028055861 1654194294 2164227199
The emergence and wide-spread use of online social networks has led to a dramatic increase on the availability of social activity data. Importantly, this data can be exploited to investigate, at a microscopic level, some of the problems that have captured the attention of economists, marketers and sociologists for decades, such as, e.g., product adoption, usage and competition. In this paper, we propose a continuous-time probabilistic model, based on temporal point processes, for the adoption and frequency of use of competing products, where the frequency of use of one product can be modulated by those of others. This model allows us to efficiently simulate the adoption and recurrent usages of competing products, and generate traces in which we can easily recognize the effect of social influence, recency and competition. We then develop an inference method to efficiently fit the model parameters by solving a convex program. The problem decouples into a collection of smaller subproblems, thus scaling easily to networks with hundred of thousands of nodes. We validate our model over synthetic and real diffusion data gathered from Twitter, and show that the proposed model does not only provides a good fit to the data and more accurate predictions than alternatives but also provides interpretable model parameters, which allow us to gain insights into some of the factors driving product adoption and frequency of use. Models of networked diffusion that are motivated by analogy with the spread of infectious disease have been applied to a wide range of social and economic adoption processes, including those related to new products, ideas, norms and behaviors. However, it is unknown how accurately these models account for the empirical structure of diffusion over networks. Here we describe the diffusion patterns arising from seven online domains, ranging from communications platforms to networked games to microblogging services, each involving distinct types of content and modes of sharing. We find strikingly similar patterns across all domains. In particular, the vast majority of cascades are small, and are described by a handful of simple tree structures that terminate within one degree of an initial adopting "seed." In addition we find that structures other than these account for only a tiny fraction of total adoptions; that is, adoptions resulting from chains of referrals are extremely rare. Finally, even for the largest cascades that we observe, we find that the bulk of adoptions often takes place within one degree of a few dominant individuals. Together, these observations suggest new directions for modeling of online adoption processes. We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of “word-of-mouth” referral. Our work builds on the observation that individuals’ decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding and leveraging this influence may thus lead to a much larger spread of the innovation than the traditional view of marketing to individuals in isolation. In this paper, we define a natural and general model of influence propagation that we term the decreasing cascade model, generalizing models used in the sociology and economics communities. In this model, as in related ones, a behavior spreads in a cascading fashion according to a probabilistic rule, beginning with a set of initially “active” nodes. We study the target set selection problem: we wish to choose a set of individuals to target for initial activation, such that the cascade beginning with this active set is as large as possible in expectation. We show that in the decreasing cascade model, a natural greedy algorithm is a 1-1 e-e approximation for selecting a target set of size k. Many people share their activities with others through online communities. These shared activities have an impact on other users' activities. For example, users are likely to become interested in items that are adopted (e.g. liked, bought and shared) by their friends. In this paper, we propose a probabilistic model for discovering latent influence from sequences of item adoption events. An inhomogeneous Poisson process is used for modeling a sequence, in which adoption by a user triggers the subsequent adoption of the same item by other users. For modeling adoption of multiple items, we employ multiple inhomogeneous Poisson processes, which share parameters, such as influence for each user and relations between users. The proposed model can be used for finding influential users, discovering relations between users and predicting item popularity in the future. We present an efficient Bayesian inference procedure of the proposed model based on the stochastic EM algorithm. The effectiveness of the proposed model is demonstrated by using real data sets in a social bookmark sharing service.