Natural graphs, such as social networks, email graphs, or instant messaging patterns, have become pervasive through the internet. These graphs are massive, often containing hundreds of millions of nodes and billions of edges. While some theoretical models have been proposed to study such graphs, their analysis is still difficult due to the scale and nature of the data. We propose a framework for large-scale graph decomposition and inference. To resolve the scale, our framework is distributed so that the data are partitioned over a sharednothing set of machines. We propose a novel factorization technique that relies on partitioning a graph so as to minimize the number of neighboring vertices rather than edges across partitions. Our decomposition is based on a streaming algorithm. It is network-aware as it adapts to the network topology of the underlying computational hardware. We use local copies of the variables and an efficient asynchronous communication protocol to synchronize the replicated values in order to perform most of the computation without having to incur the cost of network communication. On a graph of 200 million vertices and 10 billion edges, derived from an email communication network, our algorithm retains convergence properties while allowing for almost linear scalability in the number of computers.

Current graph kernels suffer from two limitations: graph kernels based on counting particular types of subgraphs ignore the relative position of these subgraphs to each other, while graph kernels based on algebraic methods are limited to graphs without node labels. In this paper we present the graphlet spectrum, a system of graph invariants derived by means of group representation theory that capture information about the number as well as the position of labeled subgraphs in a given graph. In our experimental evaluation the graphlet spectrum outperforms state-of-the-art graph kernels

This letter presents a graph kernel for spatio-spectral remote sensing image classification with support vector machines (SVMs). The method considers higher order relations in the neighborhood (beyond pairwise spatial relations) to iteratively compute a kernel matrix for SVM learning. The proposed kernel is easy to compute and constitutes a powerful alternative to existing approaches. The capabilities of the method are illustrated in several multi- and hyperspectral remote sensing images acquired over both urban and agricultural areas

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets of variables during the subset selection process, which is not available in general. Inferring group weights from data is a key open research problem in structured sparsity.In this paper, we propose a Bayesian approach to the problem of group weight learning. We model the group weights as hyperparameters of heavy-tailed priors on groups of variables and derive an approximate inference scheme to infer these hyperparameters. We empirically show that we are able to recover the model hyperparameters when the data are generated from the model, and we demonstrate the utility of learning weights in synthetic and real denoising problems