相关论文: Nonbacktracking spectral clustering of nonuniform …

Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…

Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…

We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where…

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the…

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian…

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…

We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by F\"urer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standard basis vectors and their projections onto eigenspaces of…

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations:…

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…

Statistical analysis and node clustering in hypergraphs constitute an emerging topic suffering from a lack of standardization. In contrast to the case of graphs, the concept of nodes' community in hypergraphs is not unique and encompasses…

Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s…

A panoply of multi-view clustering algorithms has been developed to deal with prevalent multi-view data. Among them, spectral clustering-based methods have drawn much attention and demonstrated promising results recently. Despite progress,…

This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain…

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…

Spectral clustering is one of the most popular graph clustering algorithms, which achieves the best performance for many scientific and engineering applications. However, existing implementations in commonly used software platforms such as…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…