Related papers: Preconditioned Spectral Clustering for Stochastic …
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
(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…
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…
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,…
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…