Nonlinear Dimensionality Reduction via Homeomorphic Tangent Space and Compactness

• 作者: Shaoqun Zhang Wanyun Xie
• 来源期刊: 国际计算机前沿大会会议论文集
• 学科: 社会科学
• 关键词: MANIFOLD LEARNING SMOOTH HOMEOMORPHISM Homeomorphic TANGENT space COMPACTNESS
• 年，卷（期）: 2017,（1）
• 页码范围: 132-133
• 页数: 2页
• 分类号: C5

摘要

This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tangent space.Then we propose a new algorithm via homeomorphic tangent space(LHTS).We also present another algorithm via compactness(CSLI)by analyzing the topological properties of manifolds.We illustrate our algorithm on the completed manifold and non-completed manifold.We also address several theoretical issues for further research and improvements.