Equivalence between LDA/QR and direct LDA

Rong Hua Li, Shuang Liang, George Baciu, Eddie Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


Singularity problems of scatter matrices in Linear Discriminant Analysis (LDA) are challenging and have obtained attention during the last decade. Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant analysis (DLDA) are two popular algorithms to solve the singularity problem. This paper establishes the equivalent relationship between LDA/QR and DLDA. They can be regarded as special cases of pseudo-inverse LDA. Similar to LDA/QR algorithm, DLDA can also be considered as a two-stage LDA method. Interestingly, the first stage of DLDA can act as a dimension reduction algorithm. The experiment compares LDA/QR and DLDA algorithms in terms of classification accuracy, computational complexity on several benchmark datasets and compares their first stages. The results confirm the established equivalent relationship and verify their capabilities in dimension reduction.
Original languageEnglish
Pages (from-to)94-112
Number of pages19
JournalInternational Journal of Cognitive Informatics and Natural Intelligence
Issue number1
Publication statusPublished - 1 Jan 2011


  • Direct LDA
  • Face Recognition
  • LDA/QR
  • Pseudo-Inverse LDA
  • Text Classification

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Artificial Intelligence


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