Local relative transformation with application to isometric embedding

Current isometric embedding approaches are topologically unstable when confronted with noisy data, as where the neighborhood is critically distorted. Based on the cognitive law, a relative transformation (RT), which improves the distinction between data points and diminishes the impact of noise on isometric embedding approaches, is proposed. As the constructed space from large scale data by RT is high-dimensional, local relative transformation (LRT) is further proposed. Subsequently, a new isometric embedding approach is developed by using LRT to construct a better neighborhood graph with fewer short-circuit edges, while the embedding is still performed in the original space. This approach has significantly increased performance and reduced running time. The proposed approach was validated by experiments on challenging benchmark data sets.