Extrinsic Principal Component Analysis
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 submanifolds 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2024
 DOI:
 10.48550/arXiv.2409.03572
 arXiv:
 arXiv:2409.03572
 Bibcode:
 2024arXiv240903572W
 Keywords:

 Statistics  Methodology