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arXiv · 1906.06451

An Infinite Dimensional Analysis of Kernel Principal Components

Palle E. T. Jorgensen·Sooran Kang·Myung-Sin Song·Feng Tian
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Abstract

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space transforms. Our results extend earlier work for probabilistic Karhunen-Lo\`eve transforms on compression of wavelet images. Our object is algorithms for optimization, selection of efficient bases, or components, which serve to minimize entropy and error; and hence to improve digital representation of images, and hence of optimal storage, and transmission. We prove several new theorems for data-dimension reduction. Moreover, with the use of frames in Hilbert space, and a new Hilbert-Schmidt analysis, we identify when a choice of Gaussian kernel is optimal.

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Palle E. T. Jorgensen, Sooran Kang, Myung-Sin Song, Feng Tian. 2019-06-15. An Infinite Dimensional Analysis of Kernel Principal Components. https://arxiv.org/abs/1906.06451

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