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中文摘要：
已有的流形学习方法仅能建立点对点的降维嵌入,而未建立高维数据流形空间与低维表示空间之间的相互映射.此缺陷已限制了流形学习方法在诸多数据挖掘问题中的进一步应用.针对这一问题,文中提出了两种新型高效的流形结构重建算法：快速算法与稳健算法.其均以经典的Isomap方法内在运行机理为出发点,进而推导出高维流形空间与低维表示空间之间双向的显式映射函数关系,基于此函数即可实现流形映射的有效重建.理论分析与实验结果证明,所提算法在计算速度、噪音敏感性、映射表现等方面相对已有方法具有明显优势.
英文摘要：
Most of the existing nonlinear dimensionality reduction methods only realize data embedding from high-dimensional to low-dimensional data spaces but not data mapping between them,which restrict their applications to approximation and prediction tasks.This paper proposes two new data mapping methods,fast method and robust method respectively,which realizes data mapping from data embedding based on the intrinsic executive mechanism of Isomap,one of the most well known nonlinear dimensionality reduction method.It also presents theoretical estimations for the approximation precision and computational complexity of the new methods.Some experiment results on synthetic and real-world data sets are demonstrated,which verifies the feasibility and effectiveness of the new data mapping methods.Particularly,the simulations,which apply the new methods on feature movie description problem and pattern classification problem,are designed.The results further shows the potential usefulness of the new methods.
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