An Extension of Principal Component Analysis
Editors: Oravec, M.
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.