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 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.
Cite
@article{arxiv.2409.03572,
title = {Extrinsic Principal Component Analysis},
author = {Ka Chun Wong and Vic Patrangenaru and Robert L. Paige and Mihaela Pricop Jeckstadt},
journal= {arXiv preprint arXiv:2409.03572},
year = {2024}
}