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Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…

Machine Learning · Statistics 2021-11-03 Michael Weylandt , George Michailidis , T. Mitchell Roddenberry

The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…

Numerical Analysis · Mathematics 2023-02-08 Lars Eldén

Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was…

Machine Learning · Computer Science 2024-12-19 Zhichang Xu , Zhiguo Long , Hua Meng

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the…

Statistics Theory · Mathematics 2017-09-14 Olga Klopp , Alexandre B. Tsybakov , Nicolas Verzelen

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…

Social and Information Networks · Computer Science 2021-10-12 Xue Gong , Desmond John Higham , Konstantinos Zygalakis

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

Optimization and Control · Mathematics 2019-08-27 Mohammadreza Chamanbaz , Giuseppe Notarstefano , Roland Bouffanais

In this survey paper it is illustrated how spectral clustering methods for unweighted graphs are adapted to the dense and sparse regimes. Whereas Laplacian and modularity based spectral clustering is apt to dense graphs, recent results show…

Combinatorics · Mathematics 2024-12-03 Marianna Bolla , Hannu Reittu , Runtian Zhou

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We…

Machine Learning · Computer Science 2026-04-23 Daniele Calandriello , Ioannis Koutis , Alessandro Lazaric , Michal Valko

The ability to tailor the spectral response of photonic devices is paramount to the advancement of a broad range of applications. The vast design space offered by disordered optical media provide enhanced functionality for spectral…

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…

Probability · Mathematics 2017-02-09 Lennart Gulikers , Marc Lelarge , Laurent Massoulié

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…

Methodology · Statistics 2021-05-05 Alexander Modell , Patrick Rubin-Delanchy

We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…

Machine Learning · Computer Science 2019-10-04 Wonpyo Park , Paul Hongsuck Seo , Bohyung Han , Minsu Cho

We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the…

Machine Learning · Computer Science 2019-03-26 Giulia Denevi , Carlo Ciliberto , Riccardo Grazzi , Massimiliano Pontil

We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-06 Sarah Cannon , Joshua J. Daymude , Cem Gokmen , Dana Randall , Andréa W. Richa

The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…

Statistics Theory · Mathematics 2017-10-24 Antoine Godichon-Baggioni , Sofiane Saadane

Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…

Data Structures and Algorithms · Computer Science 2018-12-24 Hannu Reittu , Lasse Leskelä , Tomi Räty , Marco Fiorucci

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…

Computational Engineering, Finance, and Science · Computer Science 2016-11-18 Zheng Zhang , Tarek A. El-Moselhy , Ibrahim , M. Elfadel , Luca Daniel

Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…

Probability · Mathematics 2019-09-25 Ujan Gangopadhyay , Krishanu Maulik

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

Machine Learning · Statistics 2022-08-10 Francesco Sanna Passino , Nicholas A. Heard , Patrick Rubin-Delanchy

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…

Signal Processing · Electrical Eng. & Systems 2020-12-02 David I Shuman