Geotagged data can be used to describe regions in the world and discover local themes. However, not all data produced within a region is necessarily specifically descriptive of that area. To surface the content that is characteristic for a region, we present the geographical hierarchy model (GHM), a probabilistic model based on the assumption that data observed in a region is a random mixture of content that pertains to different levels of a hierarchy. We apply the GHM to a dataset of 8 million Flickr photos in order to discriminate between content (i.e. tags) that specifically characterizes a region (e.g. neighborhood) and content that characterizes surrounding areas or more general themes. Knowledge of the discriminative and non-discriminative terms used throughout the hierarchy enables us to quantify the uniqueness of a given region and to compare similar but distant regions. Our evaluation demonstrates that our model improves upon traditional Naive Bayes classification by 47 and hierarchical TF-IDF by 27 . We further highlight the differences and commonalities with human reasoning about what is locally characteristic for a neighborhood, distilled from ten interviews and a survey that covered themes such as time, events, and prior regional knowledge.
@cite_0: 
@cite_19: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.
@cite_10: We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.
@cite_4: With the availability of cheap location sensors, geotagging of messages in online social networks is proliferating. For instance, Twitter, Facebook, Foursquare, and Google+ provide these services both explicitly by letting users choose their location or implicitly via a sensor. This paper presents an integrated generative model of location and message content. That is, we provide a model for combining distributions over locations, topics, and over user characteristics, both in terms of location and in terms of their content preferences. Unlike previous work which modeled data in a flat pre-defined representation, our model automatically infers both the hierarchical structure over content and over the size and position of geographical locations. This affords significantly higher accuracy --- location uncertainty is reduced by 40 relative to the best previous results [21] achieved on location estimation from Tweets. We achieve this goal by proposing a new statistical model, the nested Chinese Restaurant Franchise (nCRF), a hierarchical model of tree distributions. Much statistical structure is shared between users. That said, each user has his own distribution over interests and places. The use of the nCRF allows us to capture the following effects: (1) We provide a topic model for Tweets; (2) We obtain location specific topics; (3) We infer a latent distribution of locations; (4) We provide a joint hierarchical model of topics and locations; (5) We infer personalized preferences over topics and locations within the above model. In doing so, we are both able to obtain accurate estimates of the location of a user based on his tweets and to obtain a detailed estimate of a geographical language model.
Hierarchical mixture models can be used for building complex probability distributions. The underlying hierarchy, that encodes the specificity or generality of the data, might be known a priori @cite_0 or may be inferred from data by assuming a specific generative process, such as the Chinese restaurant process @cite_10 for Latent Dirichlet Allocation @cite_19 @cite_4 , where the regions and their hierarchy are learned from data. We emphasize that, in this paper, we do not try to learn latent geographical regions, but rather aim to describe regions that are known a priori. Moreover, these regions are structured according to a known hierarchy.