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Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications.

Yan-Ru Guo1, Yan-Qin Bai1, Chun-Na Li2

  • 1Department of Mathematics, Shanghai University, Shanghai, 200444 People's Republic of China.

Applied Intelligence (Dordrecht, Netherlands)
|November 12, 2021
PubMed
Summary

A new method, two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA), enhances image analysis by preserving 2D data structure. This approach improves upon existing methods for image recognition and face reconstruction tasks.

Keywords:
Bhattacharyya error boundDimensionality reductionFeature extractionRobust linear discriminant analysisTwo-dimensional linear discriminant analysis

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Area of Science:

  • Computer Vision
  • Machine Learning
  • Pattern Recognition

Background:

  • Traditional Linear Discriminant Analysis (LDA) methods convert 2D data to vectors, potentially losing structural information.
  • L2-norm linear discriminant analysis (L2BLDA) improved LDA for vector data but is not optimized for 2D inputs like images.

Purpose of the Study:

  • To introduce a novel method, two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA), specifically designed for 2D data.
  • To enhance feature extraction for image recognition and reconstruction by preserving inherent data structure.

Main Methods:

  • 2DBLDA maximizes matrix-based between-class distance and minimizes matrix-based within-class distance.
  • The method optimizes the upper bound of the Bhattacharyya error, adapting weighting constants based on the data.
  • It avoids the small sample size problem and is robust, solvable via eigenvalue decomposition.

Main Results:

  • Experimental results demonstrate the effectiveness of 2DBLDA in image recognition tasks.
  • The method also proves successful in face image reconstruction.

Conclusions:

  • 2DBLDA offers a significant advancement for analyzing 2D data, particularly in image-related applications.
  • The adaptive and robust nature of 2DBLDA makes it a valuable tool for pattern recognition challenges.