Related papers: Regularized Spectral Clustering under the Degree-C…
In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak…
Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
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.…
Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which…
Clustering is an effective tool for astronomical spectral analysis, to mine clustering patterns among data. With the implementation of large sky surveys, many clustering methods have been applied to tackle spectroscopic and photometric data…
This paper focuses on obtaining clustering information about a distribution from its i.i.d. samples. We develop theoretical results to understand and use clustering information contained in the eigenvectors of data adjacency matrices based…
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
Clustering the nodes of a graph allows the analysis of the topology of a network. The stochastic block model is a clustering method based on a probabilistic model. Initially developed for binary networks it has recently been extended to…
Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenvectors for the adjacency matrix in the $l_\infty$ norm,…
We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…
Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with…
Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…
Unsupervised clustering, also known as natural clustering, stands for the classification of data according to their similarities. Here we study this problem from the perspective of complex networks. Mapping the description of data…
This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex…
Consider a network where the nodes split into $K$ different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a…