Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

Large Graph Analysis in the GMine System

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed in an interactive environment, where human expertise can guide the process. For large graphs, though, there are some challenges: the excessive processing requirements are prohibitive, and drawing hundred-thousand nodes results in cluttered images hard to comprehend. To cope with these problems, we propose an innovative framework suited for any kind of tree-like graph visual design. GMine integrates (a) a representation for graphs organized as hierarchies of partitions - the concepts of SuperGraph and Graph-Tree; and (b) a graph summarization methodology - CEPS. Our graph representation deals with the problem of tracing the connection aspects of a graph hierarchy with sub linear complexity, allowing one to grasp the neighborhood of a single node or of a group of nodes in a single click. As a proof of concept, the visual environment of GMine is instantiated as a system in which large graphs can be investigated globally and locally

Tensorized Self-Attention: Efficiently Modeling Pairwise and Global Dependencies Together

Neural networks equipped with self-attention have parallelizable computation, light-weight structure, and the ability to capture both long-range and local dependencies. Further, their expressive power and performance can be boosted by using a vector to measure pairwise dependency, but this requires to expand the alignment matrix to a tensor, which results in memory and computation bottlenecks. In this paper, we propose a novel attention mechanism called "Multi-mask Tensorized Self-Attention" (MTSA), which is as fast and as memory-efficient as a CNN, but significantly outperforms previous CNN-/RNN-/attention-based models. MTSA 1) captures both pairwise (token2token) and global (source2token) dependencies by a novel compatibility function composed of dot-product and additive attentions, 2) uses a tensor to represent the feature-wise alignment scores for better expressive power but only requires parallelizable matrix multiplications, and 3) combines multi-head with multi-dimensional attentions, and applies a distinct positional mask to each head (subspace), so the memory and computation can be distributed to multiple heads, each with sequential information encoded independently. The experiments show that a CNN/RNN-free model based on MTSA achieves state-of-the-art or competitive performance on nine NLP benchmarks with compelling memory- and time-efficiency