Abstract: Several algorithms have been proposed to analyze the structure of high dimensional data based on the notion of manifold learning.Isomap is a representative nonlinear dimensionality reduction algorithm，which can discover low dimensional manifolds from high dimensional data.Isomap is simple but time-consuming.To speed up Isomap，L-Isomap，which uses landmark points，is proposed.But how to select landmarks is an open problem.In this paper，presents an extension of Isomap，namely WL-Isomap，which assigns data point variant weight according to the distance between it and its neighbors.Point with a higher weight has a lager probability to be selected as a landmark point.Experimental results show that WL-Isomap is more stable than L-Isomap and outper- forms L-Isomap especially when the number of landmark points is quite small.

Key words: manifold learning, dimension reduction, landmark, Isomap

摘要： 近年来出现的一系列进行维数约简的非线性方法——流形学习中等距映射（Isomap）是其中的代表，该算法高效、简单，但计算复杂度较高。基于标志点（Landmark Points）的L-Isomap减少了计算复杂度，但对于标志点的选取，大都采用随机的方法，致使该算法不稳定。考虑到样本点和近邻点相对位置，将对嵌入流形影响较大的样本点赋予较高的权重。然后根据权重大小选择标志点，同时考虑标志点之间的相对位置，使得选出的标志点不会出现过度集中的现象，近似直线分布的概率也大大降低，从而保证了算法的稳定性。实验结果表明，该算法在标志点数量较少的情况下，比L-Isomap稳定，且对缺失数据的不完整流形，也能获取和Isomap相差不大的结果。

关键词: 流形学习, 维数约简, 标志点, 等距映射