Linear discriminant dimensionality reduction

Quanquan Gu, Zhenhui Li, Jiawei Han

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


Fisher criterion has achieved great success in dimensionality reduction. Two representative methods based on Fisher criterion are Fisher Score and Linear Discriminant Analysis (LDA). The former is developed for feature selection while the latter is designed for subspace learning. In the past decade, these two approaches are often studied independently. In this paper, based on the observation that Fisher score and LDA are complementary, we propose to integrate Fisher score and LDA in a unified framework, namely Linear Discriminant Dimensionality Reduction (LDDR). We aim at finding a subset of features, based on which the learnt linear transformation via LDA maximizes the Fisher criterion. LDDR inherits the advantages of Fisher score and LDA and is able to do feature selection and subspace learning simultaneously. Both Fisher score and LDA can be seen as the special cases of the proposed method. The resultant optimization problem is a mixed integer programming, which is difficult to solve. It is relaxed into a L2,1-norm constrained least square problem and solved by accelerated proximal gradient descent algorithm. Experiments on benchmark face recognition data sets illustrate that the proposed method outperforms the state of the art methods arguably.

Original languageEnglish (US)
Title of host publicationMachine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings
Number of pages16
EditionPART 1
StatePublished - 2011
EventEuropean Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2011 - Athens, Greece
Duration: Sep 5 2011Sep 9 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6911 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


OtherEuropean Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2011

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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