Semi-supervised metric learning has attracted increasing interest in recent years. They enforce smoothness label assumption on the manifold. However, they suffer from two challenges: (1) since data in each class lies on one manifold and the similarity between classes le
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Semi-supervised metric learning has attracted increasing interest in recent years. They enforce smoothness label assumption on the manifold. However, they suffer from two challenges: (1) since data in each class lies on one manifold and the similarity between classes leads the intersection between manifolds, the smoothness assumption on the manifold is violated in intersecting regions. (2) 1NN classifier, which is applied for predicting the label of classes in metric learning methods, is suffered from the rare of labeled data and has not suitable accuracy. In this paper, a novel method for learning semi-supervised metric in the stratified space has been proposed that exploit the prior knowledge, which is the smoothness assumption on each manifold, more accurate than existing methods. In the metric learning stage, it doesn’t apply smoothness assumption on the intersecting regions and in the classification stage, labeled data in the interior regions of manifolds are extended based on the smoothness assumption. The different behavior of the Laplacian of piecewise smooth function on stratified space is exploited for the distinction of the intersecting regions from interior regions of manifolds. The results of experiments verify the improvement of the classification accuracy of the proposed method in the comparison with other methods.
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