PU Lijuan, XIE Weixin, PEI Jihong, “Valid Discriminative Null-Space for Pattern Classification,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 325-330, 2013,
Citation: PU Lijuan, XIE Weixin, PEI Jihong, “Valid Discriminative Null-Space for Pattern Classification,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 325-330, 2013,

Valid Discriminative Null-Space for Pattern Classification

Funds:  This work is supported by the National Natural Science Foundation of China (No.61071206), and the Shenzhen R&D Projects.
  • Received Date: 2012-02-01
  • Rev Recd Date: 2012-08-01
  • Publish Date: 2013-04-25
  • Linear discriminant analysis (LDA) cannot be directly applied to Small sample size problem (SSS problem). A new approach called Valid discriminative nullspace (VDNS) based on a variation of Fisher's LDA for the small sample size case is proposed. We revealed the physical meaning of the null spaces of the total scatter matrix and the within-class scatter matrix. We also analyzed the relationships of between-class scatter matrix of three subspaces: the valid subspace, the valid null space, and the valid discriminative null-space. This provides the new approach of subspace analysis-VDNS. VDNS method can project data on a lower dimensional subspace which contains valid discriminative information. Experimental results on different data sets showed that the VDNS method is superior to other relative methods in terms of recognition accuracy, robust and efficiency.
  • loading
  • J. Yang, D. Zhang, J.Y. Yang, "A generalised K-L expansion method which can deal with small sample size and highdimensional problems", Pattern Analysis & Applications, Vol.6, No.1, pp.47-54, 2003.
    H. Cevikalp, M. Wilkes, et al., "Discriminative common vectors for face recognition", IEEE Trans. Pattern Anal. Machine Intell, Vol.27, No.1, pp.4-13, 2005.
    Jian Yang and JingyuYang, "Why can LDA be performed in PCA transformed space?", Pattern Recognition, Vol.36, No.2, pp.563-566, 2003.
    Jian Yang and J.Y. Yang, "Optimal FLD algorithm for facial feature extraction", SPIE Proceedings of the Intelligent Robots and Computer Vision XX: Algorithms, Techniques, and Active Vision, Boston, MA, USA, pp.438-444, 2001.
    A.K. Qina, P.N. Suganthana, et al., "Generalized null space uncorrelated Fisher discriminant analysis for linear dimensionality reduction", Pattern Recognition, Vol.39, No.9, pp.180-1808, 2006.
    N. Vaswani and R. Chellappa, "Principal components null space analysis for image and video classification", IEEE Trans on Image Processing, Vol.15, No.7, pp.1816-1830, 2006.
    Xiaoning Song, Jingyu Yang, et al., "An optimal symmetrical null space criterion of Fisher discriminant for feature extraction and recognition", Soft Computing - A Fusion of Foundations, Methodologies and Applications, Vol.15, No.2, pp.281- 293, 2011.
    J.H. Friedman, "Regularized discriminant analysis", Journal of the American Statistical Association, Vol.84, No.405, pp.165- 175, 1989.
    Juwei Lu, K.N. Plataniotis, et al., "Regularization studies of linear discriminant analysis in small sample size scenarios with application to face recognition", Pattern Recognition Letters, Vol.26, No.2, pp.181-191, 2005.
    H. Yu and J. Yang, "A direct LDA algorithm for highdimensional data with application to face recognition", Pattern Recognition, Vol.34, No.10, pp.2067-2070, 2001.
    M. Turk and A. Pentland, "Eigenfaces for recognition", Journal Cognitive Neuroscience, Vol.3, No.1, pp.71-86, 1991.
    M. Turk and A. Pentland, "Face recognition using eigenfaces", Proceedings IEEE Confere- nce on Computer Vision and Pattern Recog- nition, Maui, HI, USA, pp.586-591, 1991.
    P.N. Belhumeur, J.P. Hespanha, et al., "Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection", IEEE Trans on Pattern Analysis and Machine Intelligence, Vol.19, No.7, pp.711-720, 1997.
    S. Theodoridis, K. Koutroumbas, "Pattern Recognition", Academic Press, London, U.K., pp.265-268, 2009.
    M. Li and B. Yuan, "2D-LDA: A novel statistical linear discriminant analysis for image matrix", Pattern Recognition Letter, Vol.26, No.5, pp.527-532, 2005.
    Wei-Shi Zhenga, J.H. Lai, et al., "1D-LDA vs. 2D-LDA: When is vector-based linear discrimi- nant analysis better than matrix-based?", Pattern Recognition, Vol.41, No.7, pp.2156- 2172, 2008.
    W. Withayachumnankul, G.M. Png, et al., "T-ray sensing and imaging", Proceedings of the IEEE, Vol.95, No.8, pp.1528-1558, 2007.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (581) PDF downloads(1032) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint