Supervised locally linear embedding in tensor space

Authors:
Chang Liu;JiLiu Zhou;Kun He;YanLi Zhu;DongFang Wang;JianPing Xia
Affiliations:
School of Computer Science, Sichuan University, Chengdu, China;School of Computer Science, Sichuan University, Chengdu, China;School of Computer Science, Sichuan University, Chengdu, China;Department of Computer Science, Henan Institute of Science and Technology, Xinxiang, China;School of Computer Science, Sichuan University, Chengdu, China;School of Computer Science, Sichuan University, Chengdu, China
Venue:
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
Year:
2009

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Abstract

The paper propose a new non-linear dimensionality reduction algorithm based on locally linear embedding called supervised locally linear embedding in tensor space (SLLE/T), in which the local manifold structure within same class are preserved and the separability between different classes is enforced by maximizing distance of each point with its neighbors. To keep structure of data, we introduce tensor representation and reduce SLLE/T into the optimization problem based on HOSVD which is desirable to solve the outofsample problem. We also prove SLLE/T can be united in the graph embedding framework. The comparison experiments on face recognition indicate that SLLE/T outperform most popular dimensionality reduction algorithms both vectorization and tensor version.