Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis regularized optimal transport (TROT). TROT interpolates a rich family of distortions from Wasserstein to Kullback-Leibler, encompassing as well Pearson, Neyman and Hellinger divergences, to name a few. We show that metric properties known for Sinkhorn-Cuturi generalize to TROT, and provide efficient algorithms for finding the optimal transportation plan with formal convergence proofs. We also present the first application of optimal transport to the problem of ecological inference, that is, the reconstruction of joint distributions from their marginals, a problem of large interest in the social sciences. TROT provides a convenient framework for ecological inference by allowing to compute the joint distribution -— that is, the optimal transportation plan itself — when side information is available, which is e.g. typically what census represents in political science. Experiments on data from the 2012 US presidential elections display the potential of TROT in delivering a faithful reconstruction of the joint distribution of ethnic groups and voter preferences.

Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present CoreCluster, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clustering algorithm. Our approach capitalizes on processing thegraph in a hierarchical manner provided by its core expansion sequence, anordered partition of the graph into different levels according to the k-coredecomposition. Such a partition provides a way to process the graph inan incremental manner that preserves its clustering structure, whilemaking the execution of the chosen clustering algorithm much faster due to thesmaller size of the graph's partitions onto which the algorithm operates.