تقرير
A kernel-based analysis of Laplacian Eigenmaps
| العنوان: | A kernel-based analysis of Laplacian Eigenmaps |
|---|---|
| المؤلفون: | Wahl, Martin |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Mathematics - Probability, Mathematics - Spectral Theory, Statistics - Machine Learning, 62H25, 60B20, 15A42, 47A55, 47D07, 35K08 |
| الوصف: | Given i.i.d. observations uniformly distributed on a closed manifold $\mathcal{M}\subseteq \mathbb{R}^p$, we study the spectral properties of the associated empirical graph Laplacian based on a Gaussian kernel. Our main results are non-asymptotic error bounds, showing that the eigenvalues and eigenspaces of the empirical graph Laplacian are close to the eigenvalues and eigenspaces of the Laplace-Beltrami operator of $\mathcal{M}$. In our analysis, we connect the empirical graph Laplacian to kernel principal component analysis, and consider the heat kernel of $\mathcal{M}$ as reproducing kernel feature map. This leads to novel points of view and allows to leverage results for empirical covariance operators in infinite dimensions. Comment: 43 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.16481 |
| رقم الأكسشن: | edsarx.2402.16481 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |