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.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Graph embedding: a general framework for dimensionality reduction


    Contributors:


    Publication date :

    2005-01-01


    Size :

    187434 byte





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding

    Rosman, G. / Bronstein, M. M. / Bronstein, A. M. et al. | British Library Online Contents | 2010


    Mixture graph based semi-supervised dimensionality reduction

    Yu, G. X. / Peng, H. / Wei, J. et al. | British Library Online Contents | 2010


    Sequential Semantic Knowledge Graph Embedding

    Shang, Yu-Ming / Huang, Heyan / Yuan, Yan | Springer Verlag | 2022


    Dimensionality reduction for probabilistic movement primitives

    Colomé Figueras, Adrià / Neumann, Gerhard / Peters, Jan et al. | BASE | 2014

    Free access