Weixin Xie 1,2*, Jihong Pei 1, and Jing Li 1,2
1 Intelligent Information Institute, Shenzhen University, Shenzhen, 518060, China
2 School of Electronic Engineering, Xidian University, Xi'an, 710071, China
*2 E-mail: firstname.lastname@example.org
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Abstract: Terahertz pulsed imaging delivers THz-TDS signals of a high dimensionality, which raises the difficulties and computations of high dimensional data process. Inspired by the applications of the projective split in "space time" physics, we apply the projective splits on THz-TDS signals and develop a new dimensionality reduction method for THz-TDS signals. In this method, THz-TDS signals are represented as vectors in a vector space of high dimension. By addition and multiplication, the vector space generates a geometric (or Clifford) algebra of the same dimension. A projective split can factorize the geometric algebra of high dimension into the geometric algebras of lower dimension. Thus, vectors of THz signals in the vector space of high dimension can similarly relate to vectors in the vector space of lower dimension. The projective splits are recursively employed and linearly map the vector space of high dimension into a sequence of sub-spaces step by step. In each step, the Principle Component Analysis (PCA) which explores statistical inherence is performed on vectors in each sub-space, and the homogenous vector of the projective split is determined by the eigenvector of the maximum principal component of PCA. In the vector space of lower dimension, as vectors related to THz-TDS signals from different substances are distant from each other, the application of substance classification and substance identification based on the relative THz-TDS signals can be easily worked out. Experiments are presented and the performance of the method is demonstrated.
Keywords: THz-TDS, Geometric algebra, Projective splits, Dimensionality reduction.
Acknowledgments: This work is supported by National Natural Science Funds of China (No. 60672153), Doctoral Subject Funds of China (No. 20060590001), and Science and Technique Project of Shenzhen (China). The THz data we used in this paper is from the open THz database of the Tera-phtonics Laboratory, RIKEN Sendai.
Cite this article:
Weixin Xie, Jihong Pei, and Jing Li. A Dimensionality Reduction Method for THz-TDS Signals via the Recursive Projective Splits Based on PCA[J]. International Journal of Terahertz Science and Technology, 2009, Vol.2, No.2: 57-67. DOI:10.11906/TST.057-067.2009.06.07