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一种新的黎曼流形学习方法 被引量：2

A novel algorithm for Riemannian manifold learning
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摘要 本文提出一种新的黎曼流形学习方法,在学习输入数据的低维流形结构的同时保持了输入数据与输出数据间的同态关系.该方法的主要思想来源于曲线坐标系中协变坐标分量的几何表达,通过把这种几何表达方式转换应用于具有流形结构的输入数据集,能够分步、线性地直接计算出它们在嵌入空间中的低维坐标.在计算的过程中使用Dijkstra算法计算各点之间的最短距离,并使用了黎曼微分几何中的一些基本概念.实验仿真分析结果表明了算法的有效性. We present a novel method for Riemannian manifold learning,which identifies the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space with homomorphism contained.The main idea is derived from the concept of covariant components in Curvilinear coordinates system.We translate this idea to a cloud of data points in order to calculate the coordinates of the points directly in a transparent way.Our implementation currently uses Dijkstra's algorithm for shortest paths in graphs and some basic concepts from Riemannian differential geometry.Experimental results show the effectiveness of the algorithm.
作者 陈绍荣 王宏强 黎湘 夏胜平
机构地区 国防科学技术大学四院一系电子科学与工程学院空间电子信息技术研究所
出处 《南京大学学报（自然科学版）》 CSCD 北大核心 2012年第1期108-114,共7页 Journal of Nanjing University（Natural Science）
基金 国家自然科学基金(60972114)
关键词 同态 黎曼流形学习 曲线坐标系 homomorphism,Riemannian manifold learning,curvilinear coordinates
分类号 O186.12 [理学—基础数学]
  • 相关文献

参考文献10

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二级参考文献14

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共引文献35

同被引文献26

  • 1TENENBAUM J B, de SILVA V, LANGFORD J C. A global geo- metric framework for nonlinear dimensionality reduction [ J]. Sci- ence, 2000, 290(5500): 2319-2323.
  • 2ROWEIS S T, SAUL L K. Nonlinear dimensionality reduction by lo- cally linear embedding [J]. Science, 2000, 290(5500): 2323- 2326.
  • 3BELKIN M, NIYOGI P. Laplacian eigenmaps for dimensionality re- duction and data representation [ J]. Neural Computation, 2003, 15 (6): 1373 -1396.
  • 4ZHANG Z, ZHA H. Principal manifolds and nonlinear dimensional- ity reduction via local tangent space alignment [ J]. SIAM Journal of Scientific Computing, 2004, 26(1): 313-338.
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南京大学学报（自然科学版）
2012年 第1期

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