Related papers: Detectability of the spectral method for sparse gr…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…

In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams. For each stream, the exact distribution is unknown, but characterized by a parameter that takes values in either of two disjoint…

Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…

We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…

Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral…

In this article, we study spectral methods for community detection based on $ \alpha$-parametrized normalized modularity matrix hereafter called $ {\bf L}_\alpha $ in heterogeneous graph models. We show, in a regime where community…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…

We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

We introduce a metric space of clusterings, where clusterings are described by a binary vector indexed by the vertex-pairs. We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the…

We prove the existence of an asymptotic phase transition threshold on community detectability for the spectral modularity method [M. E. J. Newman, Phys. Rev. E 74, 036104 (2006) and Proc. National Academy of Sciences. 103, 8577 (2006)]…

Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…