相关论文: Graph Reconstruction from Path Correlation Data
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This…
A {\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph…
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by…
Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the…
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…
We consider a multi agent optimization problem where a set of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. We focus on the case when information…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
This paper studies the problem of recovering the hidden vertex correspondence between two correlated random graphs. We propose the partially correlated Erd\H{o}s-R\'enyi graphs model, wherein a pair of induced subgraphs with a certain…
In this paper we address the problem of computing a sparse subgraph of a weighted directed graph such that the exact distances from a designated source vertex to all other vertices are preserved under bounded weight increment. Finding a…
Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
Summarizing large-scaled directed graphs into small-scale representations is a useful but less studied problem setting. Conventional clustering approaches, which based on "Min-Cut"-style criteria, compress both the vertices and edges of the…