N-Dimensional Principal Component Analysis

Part of book or chapter of book English OPEN
Yu, Hongchuan (2010)
  • Publisher: IEEE Press
  • Subject: csi

In this paper, we first briefly introduce the multidimensional Principal Component Analysis (PCA) techniques, and then amend our previous N-dimensional PCA (ND-PCA) scheme by introducing multidirectional decomposition into ND-PCA implementation. For the case of high dimensionality, PCA technique is usually extended to an arbitrary n-dimensional space by the Higher-Order Singular Value Decomposition (HO-SVD) technique. Due to the size of tensor, HO-SVD implementation usually leads to a huge matrix along some direction of tensor, which is always beyond the capacity of an ordinary PC. The novelty of this paper is to amend our previous ND-PCA scheme to deal with this challenge and further prove that the revised ND-PCA scheme can provide a near optimal linear solution under the given error bound. To evaluate the numerical property of the revised ND-PCA scheme, experiments are performed on a set of 3D volume datasets.
  • References (9)

    [1]. H. Yu and M. Bennamoun: 1D-PCA 2D-PCA to nD-PCA, Proc. of IEEE 18th Int'l Conf. on Pattern Recognition (2006), pp.181-184.

    [2]. H. Wang and N. Ahuja: Facial Expression Decomposition, Proc. of IEEE 9th Int'l Conf. on Computer Vision (2003), Vol.2.

    [3]. P. Phillips and P. Flynn et al.: Overview of the Face Recognition Grand Challenge, Proc. of CVPR2005, Vol.1.

    [4]. L. Wang and X. Wang et al.: The equivalence of two-dimensional PCA to line-based PCA, Pattern Recognition Letters, Vol.26, No.1, pp.57-60.

    [5]. J. Yang and D. Zhang et al.: Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition. IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.26, No.1, pp.131-137.

    [6]. C. Ding and J. Ye: Two-dimensional Singular Value Decomposition (2DSVD) for 2D Maps and Images, Proc.

    of SIAM Int'l Conf. Data Mining (2005), pp:32-43.

    [7]. L.D. Lathauwer, B.D. Moor and J. Vandewalle: A Multilinear Singular Value Decomposition, SIAM J. on Matrix Analysis and Applications, Vol.21, No.4, pp.1253-1278.

    [8]. M. Vasilescu, and D. Terzopoulos: Multilinear subspace analysis of image ensembles, Proc. of IEEE Conf. on Computer Vision and Pattern Recognition (2003), Vol.2.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    47
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    Bournemouth University Research Online - IRUS-UK 0 47
Share - Bookmark