High order relative transformation for isometric embedding
Isometric embedding approaches are topologically unstable when confronted with noisy or sparse data, as where the neighborhood is critically distorted. Inspired from the cognitive law, the relative transformation (RT) is defined that can be further applied to determine the better neighborhood graph for isometric embedding. Furthermore to deal with the much sparse or much noisy data, the high order relative transformation (HRT) is proposed that is then applied to enhance the isometric embedding approach by building the neighborhood graph in the high order relative space, while the embedding is still performed in the original space. HRT is simple, general, and easy to be implemented. It is also with clear physical meaning. The conducted experiments on challenging benchmark data sets validate the proposed approaches.