关键词: 维数约简, 纤维丛, 切空间, 切丛, 流形学习, 机器学习

Abstract:

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 localcharacteristics, but the overall shape of the structure of convection can be described.Especially for obvious clustering data sets , more accurate projection of the original datain the lowdimensional space can be obtained after the dimensionality reduction process. Itshows that the dimension reduction algorithm based on the tangent bundle(TB) is an effectivemethod by dimensionality reduction experiments on handwritten data and breast cancer data.

Key words: dimensionality reduction, fiber bundle, tangent space, tangent bundle, manifold learning, machine learning