Related papers: Spectral estimation for detecting low-dimensional …

Change detection in dynamic networks is an important problem in many areas, such as fraud detection, cyber intrusion detection and health care monitoring. It is a challenging problem because it involves a time sequence of graphs, each of…

Deep learning based methods have achieved remarkable success in image restoration and enhancement, but most such methods rely on RGB input images. These methods fail to take into account the rich spectral distribution of natural images. We…

An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian-matrix combined with hierarchical-clustering techniques, and…

With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the…

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…

We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…

The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is…

Estimating the number of degrees of freedom of a mechanical system or an engineering structure from the time-series of a small set of sensors is a basic problem in diagnostics, which, however, is often overlooked when monitoring their…

Hacking and false data injection from adversaries can threaten power grids' everyday operations and cause significant economic loss. Anomaly detection in power grids aims to detect and discriminate anomalies caused by cyber attacks against…

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the…

In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external…

Community detecting is one of the main approaches to understanding networks \cite{For2010}. However it has been a longstanding challenge to give a definition for community structures of networks. Here we found that community structures are…

Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on…

Spectral images captured by satellites and radio-telescopes are analyzed to obtain information about geological compositions distributions, distant asters as well as undersea terrain. Spectral images usually contain tens to hundreds of…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified…

The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…