Kernel relative transformation with applications to enhancing locally linear embedding

Locally linear embedding heavily depends on whether the neighborhood graph represents the underlying geometry structure of the data manifolds. Inspired from the cognitive law, the relative transformation(RT) and kernel relative transformation (KRT) are proposed. They can improve the distinction between data points and inhibit the impact of noise and sparsity of data, which can be then applied to construct the neighborhood graph so as to reduce the short circuit edges, while the embedding is still performed in the original space. Subsequently, another enhanced Hessian Locally Linear Embedding approach is developed with significantly increased performance. The conducted experiments on challenging benchmark data sets validate the proposed approaches.