Spectral Convergence Rate of Graph Laplacian
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 $\mathbb{R}^D$, 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.
PDF AbstractTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
