相关论文: Strong Recovery In Group Synchronization
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
Given input images, scene graph generation (SGG) aims to produce comprehensive, graphical representations describing visual relationships among salient objects. Recently, more efforts have been paid to the long tail problem in SGG; however,…
We study the problem of exact community recovery in general, two-community block models, in the presence of node-attributed $side$ $information$. We allow for a very general side information channel for node attributes, and for pairwise…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
We study the synchronized interval in undirected and unweighted random networks of coupled oscillators as a function of the number of edges. In many coupled oscillator systems, synchronization is stable in a finite interval of coupling…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…
Rotation averaging is a synchronization process on single or multiple rotation groups, and is a fundamental problem in many computer vision tasks such as multi-view structure from motion (SfM). Specifically, rotation averaging involves the…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex…
Node classification on graphs is a significant task with a wide range of applications, including social analysis and anomaly detection. Even though graph neural networks (GNNs) have produced promising results on this task, current…
We study community recovery in the planted partition model in regimes where the number and sizes of communities may vary arbitrarily with the number of vertices. In such highly unbalanced settings, standard accuracy or overlap-based metrics…
This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community…
We propose a time-varying graph signal recovery method for estimating the true time-varying graph signal from corrupted observations by leveraging dynamic graphs. Most of the conventional methods for time-varying graph signal recovery have…
The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe…
Network clustering tackles the problem of identifying sets of nodes (communities) that have similar connection patterns. However, in many scenarios, nodes also have attributes that are correlated with the clustering structure. Thus, network…
Let $G$ be a group of permutations acting on an $n$-vertex set $V$, and $X$ and $Y$ be two simple graphs on $V$. We say that $X$ and $Y$ are $G$-isomorphic if $Y$ belongs to the orbit of $X$ under the action of $G$. One can naturally…
Consider a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included iid so that the average degree is $n^\delta$. The projection of a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices…
Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…