Hierarchical linear discriminant analysis for beamforming

Jaegul Choo, Barry L. Drake, Haesun Park

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

Abstract

This paper demonstrates the applicability of the recently proposed supervised dimension reduction, hierarchical linear discriminant analysis (h-LDA) to a well-known spatial localization technique in signal processing, beamforming. The main motivation of h-LDA is to overcome the drawback of LDA that each cluster is modeled as a unimodal Gaussian distribution. For this purpose, h-LDA extends the variance decomposition in LDA to the subcluster level, and modifies the definition of the within-cluster scatter matrix. In this paper, we present an efficient h-LDA algorithm for oversampled data, where the data dimension is larger than the dimension of the data vectors. The new algorithm utilizes the Cholesky decomposition based on a generalized singular value decomposition framework. Furthermore, we analyze the data model of h-LDA by relating it to the two-way multivariate analysis of variance (MANOVA), which fits well within the context of beamforming applications. Although beamforming has been generally dealt with as a regression problem, we propose a novel way of viewing beamforming as a classification problem, and apply a supervised dimension reduction, which allows the classifier to achieve better accuracy. Our experimental results show that h-LDA out-performs several dimension reduction methods such as LDA and kernel discriminant analysis, and regression approaches such as the regularized least squares and kernelized support vector regression.

Original languageEnglish
Title of host publicationSociety for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133
Pages889-900
Number of pages12
Publication statusPublished - 2009 Dec 31
Externally publishedYes
Event9th SIAM International Conference on Data Mining 2009, SDM 2009 - Sparks, NV, United States
Duration: 2009 Apr 302009 May 2

Publication series

NameSociety for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics
Volume2

Conference

Conference9th SIAM International Conference on Data Mining 2009, SDM 2009
CountryUnited States
CitySparks, NV
Period09/4/3009/5/2

Fingerprint

Beamforming
Discriminant analysis
Discriminant Analysis
Dimension Reduction
Regression
Generalized Singular Value Decomposition
Variance Decomposition
Unimodal Distribution
Cholesky Decomposition
Multivariate Analysis of Variance
Support Vector Regression
Gaussian distribution
Singular value decomposition
Scatter
Analysis of variance (ANOVA)
Reduction Method
Classification Problems
Data Model
Data structures
Least Squares

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Software
  • Applied Mathematics

Cite this

Choo, J., Drake, B. L., & Park, H. (2009). Hierarchical linear discriminant analysis for beamforming. In Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133 (pp. 889-900). (Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics; Vol. 2).

Hierarchical linear discriminant analysis for beamforming. / Choo, Jaegul; Drake, Barry L.; Park, Haesun.

Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133. 2009. p. 889-900 (Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics; Vol. 2).

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

Choo, J, Drake, BL & Park, H 2009, Hierarchical linear discriminant analysis for beamforming. in Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133. Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics, vol. 2, pp. 889-900, 9th SIAM International Conference on Data Mining 2009, SDM 2009, Sparks, NV, United States, 09/4/30.
Choo J, Drake BL, Park H. Hierarchical linear discriminant analysis for beamforming. In Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133. 2009. p. 889-900. (Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics).
Choo, Jaegul ; Drake, Barry L. ; Park, Haesun. / Hierarchical linear discriminant analysis for beamforming. Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133. 2009. pp. 889-900 (Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics).
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