TY - GEN
T1 - Integrating global and local structures
T2 - 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
AU - Chen, Jianhui
AU - Ye, Jieping
AU - Li, Qi
PY - 2007
Y1 - 2007
N2 - Linear Discriminant Analysis (LDA) is a popular statistical approach for dimensionality reduction. LDA captures the global geometric structure of the data by simultaneously maximizing the between-class distance and minimizing the within-class distance. However, local geometric structure has recently been shown to be effective for dimensionality reduction. In this paper, a novel dimensionality reduction algorithm is proposed, which integrates both global and local structures. The main contributions of this paper include: (1) We present a least squares formulation for dimensionality reduction, which facilities the integration of global and local structures; (2) We design an efficient model selection scheme for the optimal integration, which balances the tradeoff between the global and local structures; and (3) We present a detailed theoretical analysis on the intrinsic relationship between the proposed framework and LDA. Our extensive experimental studies on benchmark data sets show that the proposed integration framework is competitive with traditional dimensionality reduction algorithms, which use global or local structure only.
AB - Linear Discriminant Analysis (LDA) is a popular statistical approach for dimensionality reduction. LDA captures the global geometric structure of the data by simultaneously maximizing the between-class distance and minimizing the within-class distance. However, local geometric structure has recently been shown to be effective for dimensionality reduction. In this paper, a novel dimensionality reduction algorithm is proposed, which integrates both global and local structures. The main contributions of this paper include: (1) We present a least squares formulation for dimensionality reduction, which facilities the integration of global and local structures; (2) We design an efficient model selection scheme for the optimal integration, which balances the tradeoff between the global and local structures; and (3) We present a detailed theoretical analysis on the intrinsic relationship between the proposed framework and LDA. Our extensive experimental studies on benchmark data sets show that the proposed integration framework is competitive with traditional dimensionality reduction algorithms, which use global or local structure only.
UR - http://www.scopus.com/inward/record.url?scp=35148833127&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=35148833127&partnerID=8YFLogxK
U2 - 10.1109/CVPR.2007.383040
DO - 10.1109/CVPR.2007.383040
M3 - Conference contribution
AN - SCOPUS:35148833127
SN - 1424411807
SN - 9781424411801
T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
BT - 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
Y2 - 17 June 2007 through 22 June 2007
ER -