Related papers: Fast Eigenspace Approximation using Random Signals
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 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…
Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform…
In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…
We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization,…
Learning a suitable graph is an important precursor to many graph signal processing (GSP) pipelines, such as graph spectral signal compression and denoising. Previous graph learning algorithms either i) make some assumptions on connectivity…
We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…
Several graph data mining, signal processing, and machine learning downstream tasks rely on information related to the eigenvectors of the associated adjacency or Laplacian matrix. Classical eigendecomposition methods are powerful when the…
The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
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 work concerns sampling of smooth signals on arbitrary graphs. We first study a structured sampling strategy for such smooth graph signals that consists of a random selection of few pre-defined groups of nodes. The number of groups to…
The random sampling on graph signals is one of the fundamental topics in graph signal processing. In this letter, we consider the random sampling of k-bandlimited signals from the local measurements and show that no more than O(klogk)…
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…
Exact eigendecomposition of large matrices is very expensive, and it is practically impossible to compute exact eigenvalues. Instead, one may set a more modest goal of approaching the empirical distribution of the eigenvalues, recovering…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…