Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

Research output: Contribution to journalJournal article – Annual report year: 2015Researchpeer-review

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We propose a general technique for obtaining sparse solutions to generalized eigenvalue problems, and call it Regularized Generalized Eigen-Decomposition (RGED). For decades, Fisher's discriminant criterion has been applied in supervised feature extraction and discriminant analysis, and it is formulated as a generalized eigenvalue problem. Thus RGED can be applied to effectively extract sparse features and calculate sparse discriminant directions for all variants of Fisher discriminant criterion based models. Particularly, RGED can be applied to matrix-based and even tensor-based discriminant techniques, for instance, 2D-Linear Discriminant Analysis (2D-LDA). Furthermore, an iterative algorithm based on the alternating direction method of multipliers is developed. The algorithm approximately solves RGED with monotonically decreasing convergence and at an acceptable speed for results of modest accuracy. Numerical experiments based on four data sets of different types of images show that RGED has competitive classification performance with existing multidimensional and sparse techniques of discriminant analysis.
Original languageEnglish
JournalPattern Recognition
Volume49
Pages (from-to)43-54
ISSN0031-3203
DOIs
Publication statusPublished - 2015
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Regularized generalized eigen-decomposition, Sparse 2D-LDA, Sparse 3D-LDA, Sparse discriminant analysis, Sparse supervised feature extraction
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