DeepAI AI Chat
Log In Sign Up

Spectral Convergence Rate of Graph Laplacian

by   Xu Wang, et al.
University of California, San Diego

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 compact submanifold M in R^D, we establish the spectral convergence rate of the graph Laplacian. It implies the consistency of the spectral clustering algorithm via a standard perturbation argument. A simple numerical study indicates the necessity of a denoising step before applying spectral algorithms.


page 1

page 2

page 3

page 4


Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities

In this paper, we give a spectral approximation result for the Laplacian...

Geometric structure of graph Laplacian embeddings

We analyze the spectral clustering procedure for identifying coarse stru...

The decomposition of the higher-order homology embedding constructed from the k-Laplacian

The null space of the k-th order Laplacian ℒ_k, known as the k-th homolo...

A New Spectral Clustering Algorithm

We present a new clustering algorithm that is based on searching for nat...

The spectral dimension of simplicial complexes: a renormalization group theory

Simplicial complexes are increasingly used to study complex system struc...

K-way p-spectral clustering on Grassmann manifolds

Spectral methods have gained a lot of recent attention due to the simpli...

Local Graph Clustering with Network Lasso

We study the statistical and computational properties of a network Lasso...