Related papers: Dual regularized Laplacian spectral clustering met…
Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the…
The paper considers the DIverse MultiPLEx (DIMPLE) network model, introduced in Pensky and Wang (2021), where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all…
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.…
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…
Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
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…
Network-based clustering methods frequently require the number of communities to be specified \emph{a priori}. Moreover, most of the existing methods for estimating the number of communities assume the number of communities to be fixed and…
Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
Directed networks are broadly used to represent asymmetric relationships among units. Co-clustering aims to cluster the senders and receivers of directed networks simultaneously. In particular, the well-known spectral clustering algorithm…
We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…
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…
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 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…
The research on complex networks has achieved significant progress in revealing the mesoscopic features of networks. Community detection is an important aspect of understanding real-world complex systems. We present in this paper a…
Multilayer and multiplex networks are becoming common network data sets in recent times. We consider the problem of identifying the common community structure for a special type of multilayer networks called multi-relational networks. We…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…