Related papers: Incremental Method for Spectral Clustering of Incr…
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 (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster.…
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
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…
We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…
This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$…
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…
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…
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…
In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and…
The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional…
This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a…
A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…
This article proposes a first analysis of kernel spectral clustering methods in the regime where the dimension $p$ of the data vectors to be clustered and their number $n$ grow large at the same rate. We demonstrate, under a $k$-class…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
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…