LAUSR

Abstract Considerable research efforts have been done in learning semi-supervised distance metric learning based on both manifold and cluster assumptions in the past few years. However, there is a major problem with them once they are applied to data lying on stratified space. The problem is that label smoothness assumption on manifold and cluster may be violated in the intersecting regions of manifolds. This problem is caused by overlearning of locality that misleads the metric learning process in the absence of enough labeled data. In this paper, we will propose a novel semi-supervised metric learning for stratified spaces (S2MLS2) which removes unsuitable local constraints in the manifold based methods for adapting to the smoothness assumption on multi manifolds. We will also impose some non-local constraints to detect the shared structures at different positions in the absence of enough supervised information. Besides, a novel bootstrapping method based on smoothness assumption on multi manifolds will be proposed to enlarge the labeled data. 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.