Related papers: Nonlinear spectral clustering with C++ GraphBLAS
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
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…
In recent years, spectral clustering has become one of the most popular clustering algorithms for image segmentation. However, it has restricted applicability to large-scale images due to its high computational complexity. In this paper, we…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…
Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a…
We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guarantees…
Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…
Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
Spectral clustering methods have gained widespread recognition for their effectiveness in clustering high-dimensional data. Among these techniques, constrained spectral clustering has emerged as a prominent approach, demonstrating enhanced…
Despite the fundamental importance of clustering, to this day, much of the relevant research is still based on ambiguous foundations, leading to an unclear understanding of whether or how the various clustering methods are connected with…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
Classical multivariate statistical methods such as covariance estimation and principal component analysis are well understood mathematically, yet their application at extreme data scales remains challenging. When the number of observations…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains…
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.…
Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on…
Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…