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 information have been utilised to enhance LDA. However, the intrinsic problems of LDA still exist and solely the similarity among the unlabeled data is utilised. In this paper, we have a tendency to propose a novel algorithm, known as Semisupervised Semi-Riemannian Metric Map (S3RMM), following the geometric framework of semi Riemannian manifolds. S3RMM 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 will also be a general framework for proposing new semisupervised algorithms, utilizing the present discrepancy-criterion-based mostly algorithms. The experiments demonstrated on faces and handwritten digits show that S3RMM is promising for semisupervised feature extraction.

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