A Unified Probabilistic Generative Model

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To model user check-in activities, we propose a unified probabilistic generative model TRM to sim- ulate the process of user’s decision-making for the selection of POIs. Figure 1 shows the graphical representation of TRM where N, K and R denote the number of users, topics and regions, re- spectively. We first introduce the notations of our model and list them in Table II. Our input data,
i.e., users’ check-in records, are modeled as observed random variables, shown as shaded circles in
Figure 1. As a POI has both semantic and geographical attributes, we introduce two latent random variables, topic z and region r, which are responsible for generating them, respectively. Based on the two latent factors, TRM aims to model and infer users’
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Thus, each topic z in TRM is not only associated with a word distribution ϕz, but also with a distribu- tion over time ψz. This design enables ϕz and ψz to be mutually influenced and enhanced during the topic discovery process, facilitating the clustering of the words of POIs with similar temporal patterns into the same topic with high probability. To integrate the check-in time information to the topic discovery process, we employ the widely adopted discretization method in [Gao et al. 2013;
Yuan et al. 2013] to split a day into hourly-based slots.
In the standard topic models [Blei et al. 2003; Wallach et al. 2009], a document (i.e., a bag of words) contains a mixture of topics, represented by a topic distribution, and each word has a hidden topic label. While this is a reasonable assumption for long documents, for short document Wv, it is most likely to be about a single topic. We therefore assign a single topic to the document Wv.
Similar idea of assigning a single topic to a twitter post has been used before [Zhao et al. 2011].
User Mobility Modeling. Different from users’ online behaviors in the virtual world, users’ check-in activities in the physical world are limited by travel distance. So, it is also importan- t to capture users’ spatial patterns (or activity ranges) according to the location distributions of their historical checked-in POIs. The spatial clustering phenomenon indicates that users are most likely to check-in a number
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