基于相对流形的局部线性嵌入

Locally Linear Embedding Based on Relative Manifold

局部线性嵌入算法极大地依赖于邻域是否真实地反映了流形的内在结构,现有方法构造的邻域结构是拓扑不稳定的,对噪音和稀疏数据敏感.根据认知的相对性规律提出了相对变换,并用其构造了相对空间和相对流形.相对变换可以提高数据之间的可区分性,并能抑制噪音和数据稀疏的影响.在构造的相对空间和相对流形上确定数据点的邻域能够更真实地反映流形的内在结构,由此提出了增强的局部线性嵌入算法,明显地提高了性能,特别是基于流形的方法还同时提高了速度.标准数据集上的实验结果验证了该方法的有效性.

Locally linear embedding greatly depends on whether the neighborhood graph can realistically reflect the underlying geometry structure of the data manifolds. The topological structure of constructed neighborhood with the existing approaches is unstable. It is sensitive to the noisy and sparse data sets. Based on the relative cognitive law, the relative transformation is presented, by which the relative space and the relative manifold are further constructed. The relative transformation can improve the distinguishing ability between data points and reduce the impact of noise and sparsity of data. To determine the neighborhood in the relative space and the relative manifold can more truly reflect the manifold structure, based on which the enhanced local linear embedding algorithms are developed with significantly improved performance. Besides, the speed is also enhanced with this approach. The experiments on challenging benchmark data sets validate the proposed approach.