Extrinsic Principal Component Analysis
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913528772820992 |
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| author | Wong, Ka Chun Patrangenaru, Vic Paige, Robert L. Jeckstadt, Mihaela Pricop |
| author_facet | Wong, Ka Chun Patrangenaru, Vic Paige, Robert L. Jeckstadt, Mihaela Pricop |
| contents | One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical space, and the resulting chord distance is used. This method helps us analyzing high, theoretically even infinite dimensional data, from a new perspective. We define the extrinsic principal sub-manifolds of a random object on a Hilbert manifold embedded in a Hilbert space, and the sample counterparts. The resulting extrinsic principal components are useful for dimension data reduction. For application, one retains a very small number of such extrinsic principal components for a shape of contour data sample, extracted from imaging data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extrinsic Principal Component Analysis Wong, Ka Chun Patrangenaru, Vic Paige, Robert L. Jeckstadt, Mihaela Pricop Methodology One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical space, and the resulting chord distance is used. This method helps us analyzing high, theoretically even infinite dimensional data, from a new perspective. We define the extrinsic principal sub-manifolds of a random object on a Hilbert manifold embedded in a Hilbert space, and the sample counterparts. The resulting extrinsic principal components are useful for dimension data reduction. For application, one retains a very small number of such extrinsic principal components for a shape of contour data sample, extracted from imaging data. |
| title | Extrinsic Principal Component Analysis |
| topic | Methodology |
| url | https://arxiv.org/abs/2409.03572 |