Graph Embedding and Extensions: A General Framework for Dimensionality Reduction Export

@article{citeulike:977695, abstract = {Over the past few decades, a large family of algorithms\^{A}¿supervised or unsupervised; stemming from statistics or geometry theory\^{A}¿has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.}, author = {Yan, Shuicheng and Xu, Dong and Zhang, Benyu and Zhang, Hong-Jiang and Yang, Qiang and Lin, S.}, citeulike-article-id = {977695}, citeulike-linkout-0 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4016549}, journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on}, keywords = {fda, manifold-learning, metric-learning}, number = {1}, pages = {40--51}, posted-at = {2008-02-03 09:13:07}, priority = {0}, title = {Graph Embedding and Extensions: A General Framework for Dimensionality Reduction}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4016549}, volume = {29}, year = {2007} }

TY - JOUR ID - citeulike:977695 L3 - citeulike-article-id:977695 N2 - Over the past few decades, a large family of algorithms¿supervised or unsupervised; stemming from statistics or geometry theory¿has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions. IS - 1 JF - Pattern Analysis and Machine Intelligence, IEEE Transactions on EP - 51 TI - Graph Embedding and Extensions: A General Framework for Dimensionality Reduction VL - 29 SP - 40 KW - fda KW - manifold-learning KW - metric-learning AU - Yan, Shuicheng AU - Xu, Dong AU - Zhang, Benyu AU - Zhang, Hong-Jiang AU - Yang, Qiang AU - Lin, S PY - 2007/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4016549 ER -