As for the discriminant analysis on nonlinear manifold

a geodesic Gabriel graph based local discriminant merging approach was proposed.Using geodesic distance to discover the intrinsic geometry of the manifold

the geodesic Gabriel graph was constructed to locate the critical local regions where the local linear discriminants would be learned.The global nonlinear discriminant was achieved by merging the multiple local discriminants.The soft margin criterion based merging algorithm assigned the best weight to each local discriminant in an iterative way and upgraded the detection accuracy stepwise.The superiority of this algorithm was confirmed by experiments both on synthesized data and face image set.