An Extension of Principal Component Analysis

This source preferred by Jian Jun Zhang and Hongchuan Yu

Authors: Yu, H. and Zhang, J.J.

Editors: Oravec, M.

Pages: 21-34

Publisher: In-Tech

ISBN: 978-953-307-060-5

In this chapter, we first briefly introduce the 1D and 2D forms of the classical Principal Component Analysis (PCA). Then, the PCA technique is further developed and extended to an arbitrary n-dimensional space by the Higher-Order Singular Value Decomposition (HO-SVD). The novelty of this chapter is to introduce the multidimensional decomposition technique into the N-dimensional PCA scheme and further prove that the proposed ND-PCA scheme can yield a near optimal linear solution under the given error bound. To evaluate the validity and performance of the proposed ND-PCA scheme, a series of experiments are performed on the FRGC 3D face range datasets.

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