Efficient model selection for regularized linear discriminant analysis

Jieping Ye, Tao Xiong, Qi Li, Ravi Janardan, Jinbo Bi, Vladimir Cherkassky, Chandra Kambhamettu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

40 Scopus citations

Abstract

Classical Linear Discriminant Analysis (LDA) is not applicable for small sample size problems due to the singularity of the scatter matrices involved. Regularized LDA (RLDA) provides a simple strategy to overcome the singularity problem by applying a regularization term, which is commonly estimated via cross-validation from a set of candidates. However, cross-validation may be computationally prohibitive when the candidate set is large. An efficient algorithm for RLDA is presented that computes the optimal transformation of RLDA for a large set of parameter candidates, with approximately the same cost as running RLDA a small number of times. Thus it facilitates efficient model selection for RLDA.An intrinsic relationship between RLDA and Uncorrelated LDA (ULDA), which was recently proposed for dimension reduction and classification is presented. More specifically, RLDA is shown to approach ULDA when the regularization value tends to zero. That is, RLDA without any regularization is equivalent to ULDA. It can be further shown that ULDA maps all data points from the same class to a common point, under a mild condition which has been shown to hold for many high-dimensional datasets. This leads to the overfitting problem in ULDA, which has been observed in several applications. Thetheoretical analysis presented provides further justification for the use of regularization in RLDA. Extensive experiments confirm the claimed theoretical estimate of efficiency. Experiments also show that, for a properly chosen regularization parameter, RLDA performs favorably in classification, in comparison with ULDA, as well as other existing LDA-based algorithms and Support Vector Machines (SVM).

Original languageEnglish (US)
Title of host publicationProceedings of the 15th ACM Conference on Information and Knowledge Management, CIKM 2006
Pages532-539
Number of pages8
DOIs
StatePublished - Dec 1 2006
Event15th ACM Conference on Information and Knowledge Management, CIKM 2006 - Arlington, VA, United States
Duration: Nov 6 2006Nov 11 2006

Publication series

NameInternational Conference on Information and Knowledge Management, Proceedings

Other

Other15th ACM Conference on Information and Knowledge Management, CIKM 2006
CountryUnited States
CityArlington, VA
Period11/6/0611/11/06

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Keywords

  • Dimension reduction
  • Linear discriminant analysis
  • Model selection
  • Regularization

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Business, Management and Accounting(all)

Cite this

Ye, J., Xiong, T., Li, Q., Janardan, R., Bi, J., Cherkassky, V., & Kambhamettu, C. (2006). Efficient model selection for regularized linear discriminant analysis. In Proceedings of the 15th ACM Conference on Information and Knowledge Management, CIKM 2006 (pp. 532-539). (International Conference on Information and Knowledge Management, Proceedings). https://doi.org/10.1145/1183614.1183691