Related papers: Spectral Inference Methods on Sparse Graphs: Theor…

Large data applications rely on storing data in massive, sparse graphs with millions to trillions of nodes. Graph-based methods, such as node prediction, aim for computational efficiency regardless of graph size. Techniques like localized…

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem.…

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…

Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics…

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even…

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…

Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…

Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

Scattering obscures information carried by wave by producing a speckle pattern, posing a common challenge across various fields, including microscopy and astronomy. Traditional methods for extracting information from speckles often rely on…

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…

Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…

Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…

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…

The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…

Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…