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arXiv · 1510.08110

Spectral Convergence Rate of Graph Laplacian

Xu Wang
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Abstract

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.

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Xu Wang. 2015-10-27. Spectral Convergence Rate of Graph Laplacian. https://arxiv.org/abs/1510.08110

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