IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p4290-4300.html
   My bibliography  Save this article

Separable linear discriminant analysis

Author

Listed:
  • Zhao, Jianhua
  • Yu, Philip L.H.
  • Shi, Lei
  • Li, Shulan

Abstract

Linear discriminant analysis (LDA) is a popular technique for supervised dimension reduction. Due to the curse of dimensionality usually suffered by LDA when applied to 2D data, several two-dimensional LDA (2DLDA) methods have been proposed in recent years. Among which, the Y2DLDA method, introduced by Ye et al. (2005), is an important development. The idea is to utilize the underlying 2D data structure to seek for an optimal bilinear transformation. However, it is found that the proposed algorithm does not guarantee convergence. In this paper, we show that the utilization of a bilinear transformation for 2D data is equivalent to modeling the covariance matrix of 2D data as separable covariance matrix. Based on this result, we propose a novel 2DLDA method called separable LDA (SLDA). The main contributions of SLDA include (1) it provides interesting theoretical relationships between LDA and some 2DLDA methods; (2) SLDA provides a building block for mixture extension; (3) unlike Y2DLDA, a neatly analytical solution can be obtained as that in LDA. Empirical results show that our proposed SLDA achieves better recognition performance than Y2DLDA while being computationally much more efficient.

Suggested Citation

  • Zhao, Jianhua & Yu, Philip L.H. & Shi, Lei & Li, Shulan, 2012. "Separable linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4290-4300.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4290-4300
    DOI: 10.1016/j.csda.2012.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312001636
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.04.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ma, Xuan & Zhao, Jianhua & Wang, Yue & Shang, Changchun & Jiang, Fen, 2023. "Robust factored principal component analysis for matrix-valued outlier accommodation and detection," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    2. Hossain, Ahmed & Beyene, Joseph & Willan, Andrew R. & Hu, Pingzhao, 2009. "A flexible approximate likelihood ratio test for detecting differential expression in microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3685-3695, August.
    3. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    4. Márton Gosztonyi & Csákné Filep Judit, 2022. "Profiling (Non-)Nascent Entrepreneurs in Hungary Based on Machine Learning Approaches," Sustainability, MDPI, vol. 14(6), pages 1-20, March.
    5. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    6. Shaheena Bashir & Edward Carter, 2010. "Penalized multinomial mixture logit model," Computational Statistics, Springer, vol. 25(1), pages 121-141, March.
    7. Park, Junyong & Park, DoHwan, 2015. "Stein’s method in high dimensional classification and applications," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 110-125.
    8. Chakraborty, Sounak, 2009. "Bayesian binary kernel probit model for microarray based cancer classification and gene selection," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4198-4209, October.
    9. Kasim Adetayo & Lin Dan & Van Sanden Suzy & Clevert Djork-Arné & Bijnens Luc & Göhlmann Hinrich & Amaratunga Dhammika & Hochreiter Sepp & Shkedy Ziv & Talloen Willem, 2010. "Informative or Noninformative Calls for Gene Expression: A Latent Variable Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-31, January.
    10. Dawit G. Tadesse & Mark Carpenter, 2019. "A method for selecting the relevant dimensions for high-dimensional classification in singular vector spaces," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 405-426, June.
    11. Masashi Hyodo & Takahiro Nishiyama, 2018. "A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 680-699, September.
    12. Brendan P. W. Ames & Mingyi Hong, 2016. "Alternating direction method of multipliers for penalized zero-variance discriminant analysis," Computational Optimization and Applications, Springer, vol. 64(3), pages 725-754, July.
    13. Matthias Bogaert & Michel Ballings & Martijn Hosten & Dirk Van den Poel, 2017. "Identifying Soccer Players on Facebook Through Predictive Analytics," Decision Analysis, INFORMS, vol. 14(4), pages 274-297, December.
    14. Tutz, Gerhard & Ramzan, Shahla, 2015. "Improved methods for the imputation of missing data by nearest neighbor methods," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 84-99.
    15. Zhang, Chunming & Fu, Haoda & Jiang, Yuan & Yu, Tao, 2007. "High-dimensional pseudo-logistic regression and classification with applications to gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 452-470, September.
    16. Daudin, Jean-Jacques & Mary-Huard, Tristan, 2008. "Estimation of the conditional risk in classification: The swapping method," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3220-3232, February.
    17. Youssef Anzarmou & Abdallah Mkhadri & Karim Oualkacha, 2023. "Sparse overlapped linear discriminant analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 388-417, March.
    18. Lambert-Lacroix, Sophie & Peyre, Julie, 2006. "Local likelihood regression in generalized linear single-index models with applications to microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2091-2113, December.
    19. M. Kathleen Kerr, 2003. "Design Considerations for Efficient and Effective Microarray Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 822-828, December.
    20. Mingue Sun, 2009. "Liquidity Risk and Financial Competition: A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis," Working Papers 0102, College of Business, University of Texas at San Antonio.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4290-4300. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.