We investigate the extent to which social ties between people can be inferred from co-occurrence in time and space: Given that two people have been in approximately the same geographic locale at approximately the same time, on multiple occasions, how likely are they to know each other? Furthermore, how does this likelihood depend on the spatial and temporal proximity of the co-occurrences? Such issues arise in data originating in both online and offline domains as well as settings that capture interfaces between online and offline behavior. Here we develop a framework for quantifying the answers to such questions, and we apply this framework to publicly available data from a social media site, finding that even a very small number of co-occurrences can result in a high empirical likelihood of a social tie. We then present probabilistic models showing how such large probabilities can arise from a natural model of proximity and co-occurrence in the presence of social ties. In addition to providing a method for establishing some of the first quantifiable estimates of these measures, our findings have potential privacy implications, particularly for the ways in which social structures can be inferred from public online records that capture individuals' physical locations over time. computer science | privacy | probabilistic models | social networks E very day, we make inferences about the social world from incomplete observations of events around us. A particular category of such inferences draws on co-occurrences in space and time-basing estimates of a social tie between two people on the fact that they were in the same geographic locale at roughly the same time. In addition to its intuitive accessibility, such reasoning has been employed in psychological studies of urban life (1) and legal analyses of the dangers of "guilt by association" (2, 3). These issues also arise naturally in online domains, including those that reflect spatio-temporal traces of their users' activities in the physical world. Despite the broad relevance of the underlying questions, however, there has been essentially no precise basis for quantifying the significance of these effects. Here we study this issue in an online setting and find that geographic co-occurrences can in fact have significant power in forming inferences about social ties: The knowledge that two people were proximate at just a few distinct locations at roughly the same times can indicate a high conditional probability that they are directly linked in the underlying social network, in the data we consider. Our results use publicly accessible spatial and temporal information from a large social media site to derive estimates of links in the online social network of the site. We also develop a probabilistic model to account for the high probabilities that are observed. In addition to providing a quantitative basis for the power of these inferences, our results have implications for the unintended leakage of private information via participation in such sites. Our analysis uses data in which individuals engage in activities at known places and times. There are many potential sources of such data, including transaction records from cell phones, public transit systems, and credit-card providers. We use a source where analogous activities are recorded publicly and online: a largescale dataset from the popular photo-sharing site Flickr. Most photos uploaded to Flickr include the time at which the photo was taken, as reported by a clock in the digital camera, and many photos are also geo-tagged with a latitude-longitude coordinate indicating where on Earth the photograph was taken. These geotags either are specified by the photographer by clicking on a map in the Flickr web site, or (increasingly) are produced by a global positioning system (GPS) receiver in the camera or cell phone. Flickr also contains a public social network, in which users specify social ties to other users. Spatio-Temporal Co-occurrences and Social Ties We define a spatiotemporal co-occurrence between two Flickr users as an instance in which they both took photos at approximately the same place and at approximately the same time. Specifically, we divide the surface of the earth into grid-like cells, each of whose side lengths span s degrees of latitude and longitude. We say that two people A and B co-occurred in a given s × s cell C, at temporal range t, if both A and B took photos geo-tagged with a location in cell C within t days of each other. Then, for a given pair of people, we count the number of distinct cells in which they had a co-occurrence at temporal range t. For example, in Fig. 1, A and B have three co-occurrences at a temporal range of 2, and four co-occurrences at a temporal range of 7. Our central question is the following: What is the probability that two people have a social tie, given that they have co-occurrences in k distinct cells at a temporal range of t? This is a question that is relevant in any setting where co-occurrences may be indicative of social ties, and we emphasize that our methodology for exploring it is a general one; because Flickr in particular provides spatio-temporal information and also an explicit listing of social ties among its users, it is a natural domain in which to compute concrete numerical answers to the question. The answers depend on three parameters: the number of co-occurrences k (indicating the amount of evidence for a social tie), together with the cell size s and temporal range t (indicating the precision of the evidence). We compute the probability as a function of these parameters by first constructing the social network of Flickr using all friendship links declared up through April 2008 and then identifying spatio-temporal co-occurrences that occurred after April 2008. In this way, and in keeping with our initial motivation, we are only identifying social ties that existed prior to the accumulation of the evidence via co-occurrences (this is explained in more detail in Discussion). Using a dataset of 38 million geo-tagged photos from Flickr (see Materials and Methods for more detail), we find (Fig. 2) that the probability of a social tie increases sharply as the number of co-occurrences k increases and the temporal range t decreases. What is perhaps most striking is not the direction of this dependence but rather the large values of the probabilities themselves relative to the baseline probability of having a social tie. Two
The method introduced in REF utilizes the number and proximity in time and space of co-occurences among pairs of individuals to infer the likelihood of a social tie between them.
Inferring social ties from geographic coincidences
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine