Semi-supervised Discriminant Analysis on Riemannian Manifold Framework

The conventional discriminant analysis algorithms based on Riemannian manifold take into account only the statistical information of labeled data and suffer from ignoring unlabeled data.Based on graph regularization,a novel algorithm,called Semi-supervised Discriminant Analysis based on Riemannian Manifold Frame(SDARMF),is presented and applied to visual classification tasks.In SDARMF,nonsingular covariance matrices are represented as points on the Riemannian manifold.The Jensen-Bregman LogDet Divergence(JBLD) between the points on the manifold as the similarity measuring is introduced.Firstly,the data are mapped onto the Riemannian tangent space where vector representations of the data are obtained.Then,a nearest neighbor graph exploiting the labeled data and the unlabeled data is constructed to capture the local geometrical structure on Riemannian tangent space and incorporated into the objective function of Fisher Geodesic Discriminant Analysis(FGDA) as a regularization term.Finally,the transformation matrix that minimizes the objective function is given and the data are classified in transformation Riemannian manifold.Experimental results on three visual classification data sets demonstrate that the proposed algorithm obtains considerable improvement in discrimination accuracy.