局部规则嵌入

引入了拓扑结构和规则拓扑结构的概念,为了寻求具有规则拓扑结构的低维数据集,构 造了拓扑结构规则性的度量,提出了保持数据集拓扑结构的局部规则嵌入方法。与LocallyLinear Embedding,LaplacianEigenmap等核特征映射方法相比,低维嵌入结果是近似规则的,与数据分类有 着更加自然的联系。最后的实例表明,与LLE和LaplacianEigenmap方法相比,该方法能更好地保持 数据集的类特性,揭示数据集的本征结构。

Locally regular embedding

The regular topological structure was introduced. For solving the low dimensional data with regular structure, the measure of the regularity was constructed and then the dimensionality reduction was brought forward. Compared with the kernel eigenmaps, for example Locally Linear Embedding(LLE) and Laplacian Eigenmap, the method makes the results approximately regular. The last results prove the theory results and show that this technique can greatly discover the topological structure of data, compared to the LLE and Laplacian Eigenmap.