Learning Semi-Riemannian Metrics for Semisupervised Feature Extraction

Wei Zhang, Zhouchen Lin, Xiaoou Tang
2011 IEEE Transactions on Knowledge and Data Engineering  
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 (S 3 RMM), following the geometric
more » ... work of semi-Riemannian manifolds. S 3 RMM 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 S 3 RMM is promising for semisupervised feature extraction.
doi:10.1109/tkde.2010.143 fatcat:oycbi3jb7rahtnxuoapulvv3v4