Semi-supervised Dimensionality Reduction

Learning semi-Riemannian metrics for semisupervised feature extraction

Abstract. We propose Semi-Supervised Semi-Riemannian Metric Map (S3RMM) using 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 learnt via semi-supervised regression. Our method can also be a general framework for proposing new semi-supervised algorithms, utilizing the existing discrepancy criterion based algorithms. The learnt projection matrix (or the corresponding low-rank inverse covariance matrix for computing Mahalanobis distances) can be used for semi-supervised classification or semi-supervised clustering. We demonstrate its effectiveness on face recognition and digit classification.



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Copyright © 2012 Wei Zhang