Related papers: Average Sensitivity of Spectral Clustering

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…

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…

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…

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…

One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…

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…

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional…

Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…

This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a…

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…

Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

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.…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…