【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(LandmarkPoints)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。更多还原

【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.更多还原