NDLI: Graph embedding: a general framework for dimensionality reduction

Content Provider	IEEE Xplore Digital Library
Author	Shuicheng Yan Dong Xu Benyu Zhang Hong-Jiang Zhang
Copyright Year	2005
Description	Author affiliation: Dept. of Inf. Eng., Chinese Univ. of Hong Kong, Shatin, China (Shuicheng Yan)
Abstract	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-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA.
Sponsorship	IEEE Comput. Soc
Starting Page	830
Ending Page	837
File Size	187434
Page Count	8
File Format	PDF
ISBN	0769523722
ISSN	10636919
DOI	10.1109/CVPR.2005.170
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-06-20
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear discriminant analysis Statistics Geometry Kernel Algorithm design and analysis Principal component analysis Laplace equations Asia Vectors Laboratories
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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