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Extrinsic Principal Component Analysis
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Statistics - Methodology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.03572
- Document Type :
- Working Paper