In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at least $1-\rho$ in at most $O(\tfrac{n}{\epsilon} \log \tfrac{1}{\rho})$ iterations, where $n$ is the number of blocks. For strongly convex functions the method converges linearly. This extends recent results of Nesterov [Efficiency of coordinate descent methods on huge-scale optimization problems, CORE Discussion Paper #2010/2], which cover the smooth case, to composite minimization, while at the same time improving the complexity by the factor of 4 and removing $\epsilon$ from the logarithmic term. More importantly, in contrast with the aforementioned work in which the author achieves the results by applying the method to a regularized version of the objective function with an unknown scaling factor, we show that this is not necessary, thus achieving true iteration complexity bounds. In the smooth case we also allow for arbitrary probability vectors and non-Euclidean norms. Finally, we demonstrate numerically that the algorithm is able to solve huge-scale $\ell_1$-regularized least squares and support vector machine problems with a billion variables.

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and obtained differ significantly between these two research areas. Despite these differences, there have been several attempts to bridge the gap between these two formalisms, and attempts to apply methods from one field in the other. The present work aims to give an overview on the research done in combining Description Logics and Formal Concept Analysis.

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.

The spatial structure of large-scale online social networks has been largely unaccessible due to the lack of available and accurate data about people’s location. However, with the recent surging popularity of location-based social services, data about the geographic position of users have been available for the first time, together with their online social connections. In this work we present a comprehensive study of the spatial properties of the social networks arising among users of three main popular online location-based services. We observe robust universal features across them: while all networks exhibit about 40% of links below 100 km, we further discover strong heterogeneity across users, with different characteristic spatial lengths of interaction across both their social ties and social triads. We provide evidence that mechanisms akin to gravity models may influence how these social connections are created over space. Our results constitute the first large-scale study to unravel the socio-spatial properties of online location-based social networks.

Twitter and other microblogs have rapidly become a significant means by which people communicate with the world and each other in near realtime. There has been a large number of studies surrounding these social media, focusing on areas such as information spread, various centrality measures, topic detection and more. However, one area which has not received much attention is trying to better understand what information is being spread and why it is being spread. This work looks to get a better understanding of what makes people spread information in tweets or microblogs through the use of retweeting. Several retweet behavior models are presented and evaluated on a Twitter data set consisting of over 768,000 tweets gathered from monitoring over 30,000 users for a period of one month. We evaluate the proposed models against each user and show how people use different retweet behavior models. For example, we find that although users in the majority of cases do not retweet information on topics that they themselves Tweet about as or from people who are "like them" (hence anti-homophily), we do find that models which do take homophily, or similarity, into account fits the observed retweet behaviors much better than other more general models which do not take this into account. We further find that, not surprisingly, people's retweeting behavior is better explained through multiple different models rather than one model.

In this work, we study the use of Twitter by House, Senate and gubernatorial candidates during the midterm (2010) elections in the U.S. Our data includes almost 700 candidates and over 690k documents that they produced and cited in the 3.5 years leading to the elections. We utilize graph and text mining techniques to analyze differences between Democrats, Republicans and Tea Party candidates, and suggest a novel use of language modeling for estimating content cohesiveness. Our findings show significant differences in the usage patterns of social media, and suggest conservative candidates used this medium more effectively, conveying a coherent message and maintaining a dense graph of connections. Despite the lack of party leadership, we find Tea Party members display both structural and language-based cohesiveness. Finally, we investigate the relation between network structure, content and election results by creating a proof-of-concept model that predicts candidate victory with an accuracy of 88.0%.

Internet memes are phenomena that rapidly gain popularity or notoriety on the Internet. Often, modifications or spoofs add to the profile of the original idea thus turning it into a phenomenon that transgresses social and cultural boundaries. It is commonly assumed that Internet memes spread virally but scientific evidence as to this assumption is scarce. In this paper, we address this issue and investigate the epidemic dynamics of 150 famous Internet memes. Our analysis is based on time series data that were collected from Google Insights, Delicious, Digg, and StumbleUpon. We find that differential equation models from mathematical epidemiology as well as simple log-normal distributions give a good account of the growth and decline of memes. We discuss the role of log-normal distributions in modeling Internet phenomena and touch on practical implications of our findings.

As online social networks expand their role beyond maintaining existing relationships, they may look to more faceted ratings to support the formation of new connections between their users. Our study focuses on one community employing faceted ratings, CouchSurfing.org, and combines data analysis of ratings, a large-scale survey, and in-depth interviews. In order to understand the ratings, we revisit the notions of friendship and trust and uncover an asymmetry: close friendship includes trust, but high levels of trust can be achieved without close friendship. To users, providing faceted ratings presents challenges, including differentiating and quantifying inherently subjective feelings such as friendship and trust, concern over a friend's reaction to a rating, and knowledge of how ratings can affect others' reputations. One consequence of these issues is the near absence of negative feedback, even though a small portion of actual experiences and privately held ratings are negative. We show how users take this into account when formulating and interpreting ratings, and discuss designs that could encourage more balanced feedback.

We perform a sentiment analysis of all tweets published on the microblogging platform Twitter in the second half of 2008. We use a psychometric instrument to extract six mood states (tension, depression, anger, vigor, fatigue, confusion) from the aggregated Twitter content and compute a six-dimensional mood vector for each day in the timeline. We compare our results to a record of popular events gathered from media and sources. We find that events in the social, political, cultural and economic sphere do have a significant, immediate and highly specific effect on the various dimensions of public mood. We speculate that large scale analyses of mood can provide a solid platform to model collective emotive trends in terms of their predictive value with regards to existing social as well as economic indicators.

Information about community structure can be useful in a variety of mobile web applications. For instance, it has been shown that community-based methods can be more effective than alternatives for routing messages in delay-tolerant networks. In this paper we present initial research that shows that information on hierarchical structures in communities can further improve the effectiveness of message routing. This is interesting because despite much previous work on the topic, there have been few concrete applications which exploit hierarchical community structure.