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Issue No. 04 - April (2011 vol. 23)
ISSN: 1041-4347
pp: 600-611
Wei Zhang , The Chinese University of Hong Kong, Hong Kong
Zhouchen Lin , Microsoft Research Asia, Beijing
Xiaoou Tang , The Chinese University of Hong Kong, Beijing
Discriminant feature extraction plays a central role in pattern recognition and classification. Linear Discriminant Analysis (LDA) is a traditional algorithm for supervised feature extraction. Recently, unlabeled data have been utilized to improve LDA. However, the intrinsic problems of LDA still exist and only the similarity among the unlabeled data is utilized. In this paper, we propose a novel algorithm, called Semisupervised Semi-Riemannian Metric Map ({\rm S}^3RMM), following the geometric framework of semi-Riemannian manifolds. {\rm S}^3RMM maximizes the discrepancy of the separability and similarity measures of scatters formulated by using semi-Riemannian metric tensors. The metric tensor of each sample is learned via semisupervised regression. Our method can also be a general framework for proposing new semisupervised algorithms, utilizing the existing discrepancy-criterion-based algorithms. The experiments demonstrated on faces and handwritten digits show that {\rm S}^3RMM is promising for semisupervised feature extraction.
Linear discriminant analysis, semisupervised learning, semi-Riemannian manifolds, feature extraction.

X. Tang, Z. Lin and W. Zhang, "Learning Semi-Riemannian Metrics for Semisupervised Feature Extraction," in IEEE Transactions on Knowledge & Data Engineering, vol. 23, no. , pp. 600-611, 2010.
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