Integrating Global and Local Structures: A Least Squares Framework for Dimensionality Reduction

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 tha...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Jianhui Chen, Jieping Ye, Qi Li
• Keywords: Computer Vision, CVPR 2007, Dimensionality Reduction, Dimensionality Reduction Algorithm, Dimensionality Reduction Algorithms, Global Geometric Structure, Local Geometric Structure