Fewer Flops at the Top: Accuracy, Diversity, and Regularization in Two-Class Collaborative Filtering

In most existing recommender systems, implicit or explicit interactions are treated as positive links and all unknown interactions are treated as negative links. The goal is to suggest new links that will be perceived as positive by users. However, as signed social networks and newer content services become common, it is important to distinguish between positive and negative preferences. Even in existing applications, the cost of a negative recommendation could be high when people are looking for new jobs, friends, or places to live. In this work, we develop novel probabilistic latent factor models to recommend positive links and compare them with existing methods on five different openly available datasets. Our models are able to produce better ranking lists and are effective in the task of ranking positive links at the top, with fewer negative links (flops). Moreover, we find that modeling signed social networks and user preferences this way has the advantage of increasing the diversity of recommendations. We also investigate the effect of regularization on the quality of recommendations, a matter that has not received enough attention in the literature. We find that regularization parameter heavily affects the quality of recommendations in terms of both accuracy and diversity

Low-Rank Matrices on Graphs: Generalized Recovery & Applications

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. Under certain circumstances, state-of-the-art algorithms provide an exact recovery for linear low-rank structures but at the expense of highly inscalable algorithms which use nuclear norm. However, the case of non-linear structures remains unresolved. We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms. We call such data matrices as \textit{Low-Rank matrices on graphs} and show that many real world datasets satisfy this assumption approximately due to underlying stationarity. Our detailed theoretical and experimental analysis unveils the power of the simple, yet very novel recovery framework \textit{Fast Robust PCA on Graphs