Improved Locally Linear Embedding by Cognitive Geometry

摘要

Locally linear embedding heavily depends on whether the neighborhood graph represents the underlying geometry structure of the data manifolds. 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 Hessian locally linear embedding, while the embedding is still performed in the original space. The conducted experiments on both synthetic and real data sets validate the approach.