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JIANGFENG CHEN AND BAOZONG YUAN

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Institute of Information Science
Beijing Jiaotong University
Beijing, 100044, China
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Linear Graph Embedding (LGE) is the linearization of graph embedding, which could explain many of the popular dimensionality reduction algorithms such as LDA, LLE and LPP. LGE algorithms have been applied in many domains successfully; however, those algorithms need a PCA transform in advance to avoid a possible singular problem. Further, LGEs are non-orthogonal and this makes them difficult to reconstruct the data. Some orthogonal LGEs have more discriminating power than their counterparts of LGEs, but the experiments imply that their robustness should be improved. Moreover, those orthogonal LGEs also need a PCA transform. Using PCA as preprocessing can reduce noise and avoid the singular problem, but some discriminative information also is abandoned. In this paper, we present an Orthogonal LGE algorithm (Orthogonal Direct LGE) to extract features from the original data set directly by solving common Eigen value problem of symmetric positive semi definite matrix. Orthogonal LGE shares the excellence of LGEs and OLGEs. Moreover, Orthogonal LGE is least-squares normalized Orthogonal, while OLGEs is not known to be optimal for LGEs in any sense. Experimental results demonstrate the effectiveness and robustness of our proposed algorithm.

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Keywords:
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linear graph embedding, face recognition, orthogonal, lpp, ODLGE

Retrieve PDF document (**201009_09.pdf**)

Received September 18, 2008; revised January 5 & August 19, 2009; accepted January 5, 2010.

Communicated by H. Y. Mark Liao.
^{*} This work was also partially supported by National Basic Research Program of China (Grant No. 2006
CB303105), the National Natural Science Foundation of China (Grant Nos. 60673109 and 60801053), Beijing
Excellent Doctoral Thesis Program (Grant No. YB20081000401), Beijing Municipal Natural Science
Foundation (Grant No. 4082025), and Doctoral Foundation of China (Grant No. 20070004037).