一种基于切丛的维数约简方法

A Dimensionality Reduction Method Based on the Tangent Bundle

本文提出了一种基于切丛的维数约简方法。流形上的切丛不但能够刻画流形局部的结构特征,而且对流形整体的结构也能够进行描述。尤其对于聚类比较明显的数据集,在降维后能够更为精确地求得原数据在低维空间中的投影。通过对手写体数据的降维实验和BreastCancer实验表明,基于切丛的维数约简方法是一种有效的降维算法。

In this paper, we propose a dimension reduction method based on the tangent bundle. The tangent bundle of the manifold can not only describe the structure of local characteristics, but the overall shape of the structure of convection can be described. Especially for obvious clustering data sets , more accurate projection of the original data in the low dimen- sional space can be obtained after the dimensionality reduction process. It shows that the dimension reduction algorithm based on the tangent bundle（TB） is an effective method by dimensionality reduction experiments on handwritten data and breast cancer data.