Learning Semi-Riemannian Metrics for Semisupervised Feature Extraction

—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 (S3 RMM), following the geometric framework of semiRiemannian manifolds. S3 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 S3 RMM is promising for se...

• Type: Journal
• Year: 2011
• Where: TKDE
• Authors: Wei Zhang, Zhouchen Lin, Xiaoou Tang
• Keywords: Algorithms, Feature Extraction, Metric Tensor, TKDE 2011