Graph embedding: a general framework for dimensionality reduction
Graph embedding: a general framework for dimensionality reduction
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DOI：
10.1109/cvpr.2005.170
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发表时间：
2005-06
期刊：
影响因子：
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通讯作者：
Shuicheng Yan;Dong Xu;Benyu Zhang;HongJiang Zhang
中科院分区：
文献类型：
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作者：
Shuicheng Yan;Dong Xu;Benyu Zhang;HongJiang Zhang
在过去的几十年中，一个大家庭的算法-监督或无监督;源于统计或几何理论-已被提出，以提供不同的解决方案的降维问题。在本文中，除了这些算法的不同动机，我们提出了一个通用的框架，图嵌入沿着其线性化和核化，这在理论上揭示了大多数以前的算法共享的基本目标。它提供了一个统一的角度来理解这些算法，即每个算法都可以被认为是直接图嵌入或其线性/核扩展的一些特定的图表征某些统计或几何属性的数据集。此外，该框架是一个通用的平台，开发新的降维算法。为此，我们提出了一种新的监督算法，边际Fisher分析（MFA），通过设计两个图，分别表征类内紧性和类间可分性的降维。MFA用每个数据点与同类相邻点之间的距离来度量类内紧性，用类间间隔来度量类间可分性，克服了传统线性判别分析算法在数据分布假设和可用投影方向方面的局限性.人工数据上的玩具问题和真实的人脸识别实验都表明了我们提出的MFA相比LDA的优越性。
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.