Graph Embedding: A General Framework for Dimensionality Reduction

In the last decades, a large family of algorithms supervised or unsupervised; stemming from statistic or geometry theory have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-cla...

• Type: Conference
• Year: 2005
• Where: CVPR
• Authors: Shuicheng Yan, Dong Xu, Benyu Zhang, HongJiang Zhang
• Keywords: Computer Vision, CVPR 2005, Data Distribution Assumptions, Dimensionality Reduction, Discriminant Analysis Algorithm, Intra-class Compactness, Marginal Fisher Analysis