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arXiv · 2409.03572

Extrinsic Principal Component Analysis

Ka Chun Wong·Vic Patrangenaru·Robert L. Paige·Mihaela Pricop Jeckstadt
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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.

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Ka Chun Wong, Vic Patrangenaru, Robert L. Paige, Mihaela Pricop Jeckstadt. 2024-09-05. Extrinsic Principal Component Analysis. https://arxiv.org/abs/2409.03572

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