From Twitter to Facebook to Reddit, users have become accustomed to sharing the articles they read with friends or followers on their social networks. While previous work has modeled what these shared stories say about the user who shares them, the converse question remains unexplored: what can we learn about an article from the identities of its likely readers? To address this question, we model the content of news articles and blog posts by attributes of the people who are likely to share them. For example, many Twitter users describe themselves in a short profile, labeling themselves with phrases such as "vegetarian" or "liberal." By assuming that a user's labels correspond to topics in the articles he shares, we can learn a labeled dictionary from a training corpus of articles shared on Twitter. Thereafter, we can code any new document as a sparse non-negative linear combination of user labels, where we encourage correlated labels to appear together in the output via a structured sparsity penalty.

Although spectral clustering has enjoyed considerable empirical success in machine learning, its theoretical properties are not yet fully developed. We analyze the performance of a spectral algorithm for hierarchical clustering and show that on a class of hierarchically structured similarity matrices, this algorithm can tolerate noise that grows with the number of data points while still perfectly recovering the hierarchical clusters with high probability. We additionally improve upon previous results for k-way spectral clustering to derive conditions under which spectral clustering makes no mistakes. Further, using minimax analysis, we derive tight upper and lower bounds for the clustering problem and compare the performance of spectral clustering to these information theoretic limits. We also present experiments on simulated and real world data illustrating our results.