Incremental Linear Discriminant Analysis: A Fast Algorithm and Comparisons

Delin Chu, Lizhi LIAO, Kwok Po NG, Xiaoyan Wang

Research output: Contribution to journalJournal articlepeer-review

63 Citations (Scopus)


It has always been a challenging task to develop a fast and an efficient incremental linear discriminant analysis (ILDA) algorithm. For this purpose, we conduct a new study for linear discriminant analysis (LDA) in this paper and develop a new ILDA algorithm. We propose a new batch LDA algorithm called LDA/QR. LDA/QR is a simple and fast LDA algorithm, which is obtained by computing the economic QR factorization of the data matrix followed by solving a lower triangular linear system. The relationship between LDA/QR and uncorrelated LDA (ULDA) is also revealed. Based on LDA/QR, we develop a new incremental LDA algorithm called ILDA/QR. The main features of our ILDA/QR include that: 1) it can easily handle the update from one new sample or a chunk of new samples; 2) it has efficient computational complexity and space complexity; and 3) it is very fast and always achieves competitive classification accuracy compared with ULDA algorithm and existing ILDA algorithms. Numerical experiments based on some real-world data sets demonstrate that our ILDA/QR is very efficient and competitive with the state-of-the-art ILDA algorithms in terms of classification accuracy, computational complexity, and space complexity.

Original languageEnglish
Article number7027215
Pages (from-to)2716-2735
Number of pages20
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number11
Publication statusPublished - 1 Nov 2015

Scopus Subject Areas

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

User-Defined Keywords

  • Classification accuracy
  • computational complexity
  • incremental linear discriminant analysis (ILDA)
  • linear discriminant analysis (LDA).


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