Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which the chosen diffusion captures a typically unknown label propagation mechanism, that can be specific to the underlying graph, and potentially different for each class. The present work introduces a disciplined, data-efficient approach to learning classspecific diffusion functions adapted to the underlying network topology. The novel learning approach leverages the notion of "landing probabilities" of class-specific random walks, which can be computed efficiently, thereby ensuring scalability to large graphs. This is supported by rigorous analysis of the properties of the model as well as the proposed algorithms. Furthermore, a robust version of the classifier facilitates learning even in noisy environments. Classification tests on real networks demonstrate that adapting the diffusion function to the given graph and observed labels, significantly improves the performance over fixed diffusions; reaching -and many times surpassing -the classification accuracy of computationally heavier state-of-theart competing methods, that rely on node embeddings and deep neural networks.

The present work introduces the hybrid consensus alternating direction method of multipliers (H-CADMM), a novel framework for optimization over networks which unifies existing distributed optimization approaches, including the centralized and the decentralized consensus ADMM. H-CADMM provides a flexible tool that leverages the underlying graph topology in order to achieve a desirable sweet spot between node-to-node communication overhead and rate of convergence-thereby alleviating known limitations of both C-CADMM and D-CADMM. A rigorous analysis of the novel method establishes linear convergence rate and also guides the choice of parameters to optimize this rate. The novel hybrid update rules of H-CADMM lend themselves to "in-network acceleration" that is shown to effect considerable-and essentially "free-of-charge"-performance boost over the fully decentralized ADMM. Comprehensive numerical tests validate the analysis and showcase the potential of the method in tackling efficiently, widely useful learning tasks.

We introduce E R ; a versatile and efficient Latent-Factor framework for Top-N Recommendations that includes the well-known PureSVD algorithm as a special case. E R builds a low dimensional model of an inter-item proximity matrix that combines a similarity component, with a scaling operator, designed to control the influence of the prior item popularity on the final model. Seeing PureSVD within our framework provides intuition about its inner workings, exposes its inherent limitations, and also, paves the path towards painlessly improving its recommendation performance. A comprehensive set of experiments on the MovieLens and the Yahoo datasets based on widely applied performance metrics, indicate that E R outperforms several state-of-the-art algorithms, in terms of Standard and Long-Tail recommendation accuracy, exhibiting low susceptibility to sparsity, even in its most extreme manifestations -the Cold-Start problems. At the same time E R has an attractive computational profile and it can apply readily in large-scale recommendation settings.

No abstract