### 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 language | English |
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Title of host publication | Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133 |

Pages | 889-900 |

Number of pages | 12 |

Publication status | Published - 2009 Dec 31 |

Externally published | Yes |

Event | 9th SIAM International Conference on Data Mining 2009, SDM 2009 - Sparks, NV, United States Duration: 2009 Apr 30 → 2009 May 2 |

### Publication series

Name | Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics |
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Volume | 2 |

### Conference

Conference | 9th SIAM International Conference on Data Mining 2009, SDM 2009 |
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Country | United States |

City | Sparks, NV |

Period | 09/4/30 → 09/5/2 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Software
- Applied Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Hierarchical linear discriminant analysis for beamforming

AU - Choo, Jaegul

AU - Drake, Barry L.

AU - Park, Haesun

PY - 2009/12/31

Y1 - 2009/12/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=72749123797&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:72749123797

SN - 9781615671090

T3 - Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics

SP - 889

EP - 900

BT - Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133

ER -