Relative transformation-based neighborhood optimization for isometric embedding

Isometric embedding approaches can nicely deal with noiseless data sets, but they are topologically unstable when confronted with sparse data sets or with data sets containing a large amount of noise and outliers, as where the neighborhood is critically distorted. Inspired from the cognitive relativity, this paper proposes a relative transformation that can be applied to build the relative space from the original space of data. In relative space, the noise and outliers will become further away from the normal points, while the near points will become relative closer. Accordingly we determine the neighborhood in the relative space for isometric embedding, while the embedding is still performed in the original space. The conducted experiments on both synthetic and real data sets validate the approach.