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Graph embedding: a general framework for dimensionality reduction. CVPR (2005)
| Citations: | 57 - 8 self |
BibTeX
@MISC{Xu05graphembedding:,
author = {Dong Xu and Benyu Zhang and Hong-jiang Zhang},
title = {Graph embedding: a general framework for dimensionality reduction. CVPR},
year = {2005}
}
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Abstract
In the last decades, a large family of algorithmsũ supervised or unsupervised; stemming from statistic or geometry theoryũhave been proposed to provide dif-ferent solutions to the problem of dimensionality reduc-tion. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and ker-nelization, which in theory reveals the underlying objec-tive 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 spe-cific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimen-sionality reduction. To this end, we propose a new su-pervised 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 in-tra-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 direc-tions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA. 1.
Keyphrases
dimensionality reduction general framework graph embedding inter-class separability real face recognition experiment dimen-sionality reduction last decade previous algorithm theory reveals spe-cific graph toy problem in-tra-class compactness class margin data distribution assumption geometry theory different motivation direct graph embedding neighboring point traditional linear discriminant analysis algorithm general platform large family dimensionality reduc-tion data point geometry property artificial data marginal fisher analysis data set linear kernel extension available projection direc-tions new algorithm intra-class compactness new su-pervised algorithm dif-ferent solution unified perspective
