保持拓扑结构的低维嵌入

DIMENSION REDUCTION WITH ORIGINAL TOPOLOGICAL STRUCTURE

引入了拓扑邻域、拓扑结构和规则拓扑结构的概念。对拓扑邻域进行了理论分析,说明其是自适应的,随着维数的不断升高,趋于平凡拓扑邻域。为了寻求具有规则拓扑结构的低维数据集,构造了数据结构规则性的度量,提出了保持数据集拓扑结构不变的降维方法。该方法是节省参数的,降维结果是近似规则的。结果表明,它能更好的揭示数据集的结构。

The topological neighborhood, topological structure and regular structure are introduced. It is proved that the topological neigh- borhood is self-adaptive and goes to triviality with the increase of the dimension. To get the low dimensional data with regular structure, the measure of the regularity is constructed and then the dimension reduction is brought forward. The method economizes the parameters and makes the results approximately regular. The results show that this technique can well reveal the topological structure of data.