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Article
De-Biasing Covariance-Regularized Discriminant Analysis
Proceedings of the 27th International Joint Conference on Artificial Intelligence (2018, Stockholm, Sweden)
  • Haoyi Xiong, Missouri University of Science and Technology
  • Wei Cheng
  • Yanjie Fu, Missouri University of Science and Technology
  • Wenqing Hu, Missouri University of Science and Technology
  • Jiang Bian
  • Zhishan Guo, Missouri University of Science and Technology
Abstract

Fisher's Linear Discriminant Analysis (FLD) is a well-known technique for linear classification, feature extraction and dimension reduction. The empirical FLD relies on two key estimations from the data - the mean vector for each class and the (inverse) covariance matrix. To improve the accuracy of FLD under the High Dimension Low Sample Size (HDLSS) settings, Covariance-Regularized FLD (CRLD) has been proposed to use shrunken covariance estimators, such as Graphical Lasso, to strike a balance between biases and variances. Though CRLD could obtain better classification accuracy, it usually incurs bias and converges to the optimal result with a slower asymptotic rate. Inspired by the recent progress in de-biased Lasso, we propose a novel FLD classifier, DBLD, which improves classification accuracy of CRLD through de-biasing. Theoretical analysis shows that DBLD possesses better asymptotic properties than CRLD. We conduct experiments on both synthetic datasets and real application datasets to confirm the correctness of our theoretical analysis and demonstrate the superiority of DBLD over classical FLD, CRLD and other downstream competitors under HDLSS settings.

Meeting Name
27th International Joint Conference on Artificial Intelligence, IJCAI-18 (2018: July 13-19, Stokholm, Sweden)
Department(s)
Computer Science
Second Department
Mathematics and Statistics
Research Center/Lab(s)
Intelligent Systems Center
Keywords and Phrases
  • Artificial intelligence,
  • Discriminant analysis,
  • Inverse problems,
  • Asymptotic properties,
  • Classification accuracy,
  • Dimension reduction,
  • Fisher's linear discriminant analysis,
  • Linear classification,
  • Real applications,
  • Regularized discriminant analysis,
  • Synthetic datasets,
  • Covariance matrix
International Standard Book Number (ISBN)
978-0-9992411-2-7
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2018 International Joint Conferences on Artificial Intelligence, All rights reserved.
Publication Date
7-1-2018
Publication Date
01 Jul 2018
Citation Information
Haoyi Xiong, Wei Cheng, Yanjie Fu, Wenqing Hu, et al.. "De-Biasing Covariance-Regularized Discriminant Analysis" Proceedings of the 27th International Joint Conference on Artificial Intelligence (2018, Stockholm, Sweden) (2018) p. 2889 - 2897 ISSN: 1045-0823
Available at: http://works.bepress.com/wenqing-hu/4/