【摘要】 为处理极度弯曲的数据流形,提出了基于局部测地距离估计的Hessian局部线性嵌入算法.算法采用Hessian局部线性嵌入(HLLE)的概念框架,采用局部估计的测地距离而不是欧氏距离来确定每个点的邻域,从而减少数据流形弯曲对邻域选择的影响.算法可认为是全局和局部方法的综合,在性能上不仅比HLLE显著提高,有更强的鲁棒性,而且时间增加不明显.标准数据集上的实验结果验证了所提方法的有效性.更多还原

【Abstract】 To deal with highly curved data manifolds,the Hessian locally linear embedding(HLLE) algorithm was modified based on a locally estimated geodesic distance.It used the general conceptual framework of HLLE to guarantee correct setting of local isometry to an open connected subset.It employs the locally estimated geodesic distance instead of the Euclidean distance to determine the neighborhood of any point,so that it reduces the distorting influence of curvature of the data manifold on determining the neighborhood.This approach can be regarded as the integration of a local method and a global method,so that it has better performance and stability than HLLE,with only a slight increase in computational time.Experiments conducted on benchmark data sets verified etficioncy of the proposed approach.更多还原