Skip to main content
padlock icon - secure page this page is secure

Sparse discriminant analysis based on estimation of posterior probabilities

Buy Article:

$61.00 + tax (Refund Policy)

Fisher's linear discriminant analysis (FLDA) is known as a method to find a discriminative feature space for multi-class classification. As a theory of extending FLDA to an ultimate nonlinear form, optimal nonlinear discriminant analysis (ONDA) has been proposed. ONDA indicates that the best theoretical nonlinear map for maximizing the Fisher's discriminant criterion is formulated by using the Bayesian a posterior probabilities. In addition, the theory proves that FLDA is equivalent to ONDA when the Bayesian a posterior probabilities are approximated by linear regression (LR). Due to some limitations of the linear model, there is room to modify FLDA by using stronger approximation/estimation methods. For the purpose of probability estimation, multi-nominal logistic regression (MLR) is more suitable than LR. Along this line, in this paper, we develop a nonlinear discriminant analysis (NDA) in which the posterior probabilities in ONDA are estimated by MLR. In addition, in this paper, we develop a way to introduce sparseness into discriminant analysis. By applying L1 or L2 regularization to LR or MLR, we can incorporate sparseness in FLDA and our NDA to increase generalization performance. The performance of these methods is evaluated by benchmark experiments using last_exam17 standard datasets and a face classification experiment.
No Reference information available - sign in for access.
No Citation information available - sign in for access.
No Supplementary Data.
No Article Media
No Metrics

Keywords: Fisher's discriminant analysis; linear regression; logistic regression; optimal nonlinear discriminant analysis; sparse discriminant analysis

Document Type: Research Article

Affiliations: 1: School of Science and Engineering, Tokyo Denki University, Saitama, Japan 2: Intelligent Systems Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba-shi, Japan 3: Department of Information Engineering, Hiroshima University, Hiroshima, Japan

Publication date: November 18, 2019

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more