相关论文: Power-Law Graph Cuts

It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…

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…

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…

We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking…

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…

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…

Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

Clustering analysis has been widely used in trust evaluation on various complex networks such as wireless sensors networks and online social networks. Spectral clustering is one of the most commonly used algorithms for graph-structured data…

Explainable clustering by axis-aligned decision trees was introduced by Moshkovitz et al. (2020) and has gained considerable interest. Prior work has focused on minimizing the price of explainability for specific clustering objectives,…

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…

Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability.…