Related papers: On Consistency of Compressive Spectral Clustering

This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…

Mixed membership community detection is a challenge problem in network analysis. To estimate the memberships and study the impact of regularized spectral clustering under the mixed membership stochastic block (MMSB) model, this article…

Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was…

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…

The community detection problem on multilayer networks have drawn much interest. When the nodal covariates ar also present, few work has been done to integrate information from both sources. To leverage the multilayer networks and the…

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…

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…

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 algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…

Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…

In a graph bisection problem, we are given a graph $G$ with two equally-sized unlabeled communities, and the goal is to recover the vertices in these communities. A popular heuristic, known as spectral clustering, is to output an estimated…

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small…

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…

Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…

Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…