Abstract

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.