主流形和非线性维数化简的切向空间校正

• 作 者: 张振跃 查宏远
• 机 构: Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou 310027, P. R. ChinaDepartmen
• 出 处: 上海大学学报（英文版）
• 发表日期: 2004年4期
• 关键词: nonlinear dimensionality reduction principal manifold tangent space subspace ali

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.