When Locally Linear Embedding Hits Boundary
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914848863944704 |
|---|---|
| author | Wu, Hau-tieng Wu, Nan |
| author_facet | Wu, Hau-tieng Wu, Nan |
| contents | Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algorithm which is a potential approach to recover the Dirichlet Laplace-Beltrami operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_04423 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | When Locally Linear Embedding Hits Boundary Wu, Hau-tieng Wu, Nan Statistics Theory 62-07 Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algorithm which is a potential approach to recover the Dirichlet Laplace-Beltrami operator. |
| title | When Locally Linear Embedding Hits Boundary |
| topic | Statistics Theory 62-07 |
| url | https://arxiv.org/abs/1811.04423 |