Semi-supervised metric learning in stratified spaces via intergrating local constraints and information-theoretic non-local constraints

The proposed algorithm is based on different behavior of Laplacian of piecewise-smooth function on multi manifolds in the neighborhood of non-interior points of the manifolds as compared with interior points of the manifolds. Experiments on artificial and real benchmark data sets demonstrate that the proposed metric learning method outperforms many state-of-the-art metric learning methods.