Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914437984681984 |
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| author | Kohli, Dhruv He, Jesse Holtz, Chester Cloninger, Alexander Mishne, Gal |
| author_facet | Kohli, Dhruv He, Jesse Holtz, Chester Cloninger, Alexander Mishne, Gal |
| contents | This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly stochastic scaling of the Gaussian heat kernel via Sinkhorn iterations to this setting. Our main contributions are: (a) deriving a characterization of the scaling factors for manifolds with boundary, (b) developing a boundary direction estimator aimed at identifying boundary points followed by a boundary-corrected kernel density estimator based on doubly stochastic kernel and local principal component analysis, and (c) demonstrating through simulations that the resulting estimates of the boundary points and the sampling density outperform the standard Gaussian kernel-based approach, particularly under noisy conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel Kohli, Dhruv He, Jesse Holtz, Chester Cloninger, Alexander Mishne, Gal Statistics Theory Differential Geometry This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly stochastic scaling of the Gaussian heat kernel via Sinkhorn iterations to this setting. Our main contributions are: (a) deriving a characterization of the scaling factors for manifolds with boundary, (b) developing a boundary direction estimator aimed at identifying boundary points followed by a boundary-corrected kernel density estimator based on doubly stochastic kernel and local principal component analysis, and (c) demonstrating through simulations that the resulting estimates of the boundary points and the sampling density outperform the standard Gaussian kernel-based approach, particularly under noisy conditions. |
| title | Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel |
| topic | Statistics Theory Differential Geometry |
| url | https://arxiv.org/abs/2411.18942 |