Generalized linear discriminant analysis: A unified framework and efficient model selection

Shuiwang Ji, Jieping Ye

Research output: Contribution to journalArticlepeer-review

163 Scopus citations


High-dimensional data are common in many domains, and dimensionality reduction is the key to cope with the curse-of-dimensionality. Linear discriminant analysis (LDA) is a well-known method for supervised dimensionality reduction. When dealing with high-dimensional and low sample size data, classical LDA suffers from the singularity problem. Over the years, many algorithms have been developed to overcome this problem, and they have been applied successfully in various applications. However, there is a lack of a systematic study of the commonalities and differences of these algorithms, as well as their intrinsic relationships. In this paper, a unified framework for generalized LDA is proposed, which elucidates the properties of various algorithms and their relationships. Based on the proposed framework, we show that the matrix computations involved in LDA-based algorithms can be simplified so that the cross-validation procedure for model selection can be performed efficiently. We conduct extensive experiments using a collection of high-dimensional data sets, including text documents, face images, gene expression data, and gene expression pattern images, to evaluate the proposed theories and algorithms.

Original languageEnglish (US)
Pages (from-to)1768-1782
Number of pages15
JournalIEEE Transactions on Neural Networks
Issue number10
StatePublished - 2008


  • Dimensionality reduction
  • Linear discriminant analysis (LDA)
  • Model selection
  • Principal component analysis (PCA)
  • Regularization
  • Visualization

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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