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We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

Computer Vision and Pattern Recognition · Computer Science 2016-01-12 Jörg Hendrik Kappes , Paul Swoboda , Bogdan Savchynskyy , Tamir Hazan , Christoph Schnörr

We prove strong consistency of spectral clustering under the degree-corrected hypergraph stochastic block model in the sparse regime where the maximum expected hyperdegree is as small as $\Omega(\log n)$ with $n$ denoting the number of…

Social and Information Networks · Computer Science 2025-03-11 Chong Deng , Xin-Jian Xu , Shihui Ying

Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…

Data Structures and Algorithms · Computer Science 2023-10-18 Peter Macgregor

We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…

Discrete Mathematics · Computer Science 2021-03-22 Timothy D. Goodrich , Eric Horton , Blair D. Sullivan

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering…

Machine Learning · Computer Science 2021-11-29 Dimosthenis Pasadakis , Christie Louis Alappat , Olaf Schenk , Gerhard Wellein

Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric…

Data Structures and Algorithms · Computer Science 2021-03-10 Fatih Taşyaran , Berkay Demireller , Kamer Kaya , Bora Uçar

As the most typical graph clustering method, spectral clustering is popular and attractive due to the remarkable performance, easy implementation, and strong adaptability. Classical spectral clustering measures the edge weights of graph…

Machine Learning · Computer Science 2023-12-08 Dehua Peng , Zhipeng Gui , Huayi Wu

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…

Machine Learning · Computer Science 2024-02-05 Hongyu Zhu , Stefan Klus , Tuhin Sahai

We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…

Data Structures and Algorithms · Computer Science 2010-07-22 Daniel A. Spielman , Shang-Hua Teng

Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral…

Machine Learning · Computer Science 2021-09-08 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Graph partitioning (GP) is a classic problem that divides the node set of a graph into densely-connected blocks. Following the IEEE HPEC Graph Challenge and recent advances in pre-training techniques (e.g., large-language models), we…

Machine Learning · Computer Science 2024-09-04 Meng Qin , Chaorui Zhang , Yu Gao , Yibin Ding , Weipeng Jiang , Weixi Zhang , Wei Han , Bo Bai

We present a sequential Bayesian learning method for tracking non-stationary signal-to-noise ratios in LDPC codes using probabilistic graphical models. We represent the LDPC code as a cluster graph using a general purpose cluster graph…

Signal Processing · Electrical Eng. & Systems 2023-10-03 J du Toit , J du Preez , R Wolhuter

Transform-domain least mean squares (LMS) adaptive filters encompass the class of algorithms where the input data are subjected to a data-independent unitary transform followed by a power normalization stage as preprocessing steps. Because…

Signal Processing · Electrical Eng. & Systems 2020-12-29 Tamal Batabyal , Daniel S. Weller , Jaideep Kapur , Scott T. Acton

Graph partitioning plays a vital role in distributedlarge-scale web graph analytics, such as pagerank and labelpropagation. The quality and scalability of partitioning strategyhave a strong impact on such communication- and…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-01-04 Deyu Kong , Xike Xie , Zhuoxu Zhang

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is a NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the…

Analysis of PDEs · Mathematics 2024-10-08 Antonio Corbo Esposito , Gianpaolo Piscitelli

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

Data Structures and Algorithms · Computer Science 2023-08-31 Marcelo Fonseca Faraj

Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-22 Alkida Balliu , Sebastian Brandt , Manuela Fischer , Rustam Latypov , Yannic Maus , Dennis Olivetti , Jara Uitto

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…

Machine Learning · Computer Science 2023-02-07 Jinyu Cai , Yi Han , Wenzhong Guo , Jicong Fan

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…

We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of…

Data Structures and Algorithms · Computer Science 2025-03-05 Xingzi Xu , Tuhin Sahai