Related papers: Spectral concentration and greedy k-clustering
We consider the problem of online graph colouring. Whenever a node is requested, a colour must be assigned to the node, and this colour must be different from the colours of any of its neighbours. According to the greedy algorithm the node…
In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cut refinement on each level of the hierarchy. Multilevel partitioners are…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…
The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…
Spectral clustering is one of the most popular clustering algorithms that has stood the test of time. It is simple to describe, can be implemented using standard linear algebra, and often finds better clusters than traditional clustering…
This work concerns sampling of smooth signals on arbitrary graphs. We first study a structured sampling strategy for such smooth graph signals that consists of a random selection of few pre-defined groups of nodes. The number of groups to…
The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this…
We describe the Greedy Sparse Subspace Clustering (GSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces from incomplete corrupted and noisy data. We provide…
Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
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…
Spectral embedding of graphs uses the top k non-trivial eigenvectors of the random walk matrix to embed the graph into R^k. The primary use of this embedding has been for practical spectral clustering algorithms [SM00,NJW02]. Recently,…