摘要： 高维非线性数据的降维处理对于计算机完成高复杂度的数据源分析是非常重要的。从拓扑学角度分析，维数约简的过程是挖掘嵌入在高维数据中的低维线性或非线性的流形。该文在局部嵌入思想的流形学习算法的基础上，提出直接估计梯度值的方法，从而达到局部线性误差逼近最小化，实现高维非线性数据的维数约简，并在Swiss roll曲线上采样测试取得了良好的降维效果。

关键词: 直接估计梯度, 降维算法, 流形学习, 局部嵌入

Abstract: The dimensionality reduction techniques are very important for high-dimensional nonlinear data to complete the processing and analysis of the high complexity data source. From the view of topology, the process of dimensionality reduction is to find a low-dimensional linear or nonlinear manifold embedded in the high-dimensional data. On the basis of locally embedding manifold learning algorithms, a data dimensionality reduction algorithm based on direct estimate grads is proposed. The dimensionality reduction of the high-dimensionality nonlinear data is achieved by locally linear error approximating minimum. The simulation results of Swiss roll curse sampling and test show the significant effectiveness of the proposed algorithm.

Key words: direct estimate grads, dimensionality reduction algorithm, manifold learning, locally embedding

中图分类号: 

• TP391