Related papers: Regularized Spectral Clustering under the Degree-C…
Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to…
Modern network datasets are often composed of multiple layers, either as different views, time-varying observations, or independent sample units, resulting in collections of networks over the same set of vertices but with potentially…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$…
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden…
Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…
Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…
Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…
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…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is…
Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix…
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…