邻域参数动态变化的局部线性嵌入

局部线性嵌入是最有竞争力的非线性降维方法,有较强的表达能力和计算优势.但它们都采用全局一致的邻城大小,只适用于均匀分布的流形,无法处理现实中大量存在的非均匀分布流形.为此,提出一种邻域大小动态确定的新局部线性嵌入方法.它采用Hessian局部线性嵌入的概念框架,但用每个点的局部邻域估计此邻域内任意点之间的近似测地距离,然后根据近似测地距离与欧氏距离之间的关系动态确定该点的邻域大小,并以此邻域大小构造新的局部邻域.算法几何意义清晰,在观察数据稀疏和数据带噪音等情况下,都比现有算法有更强的鲁棒性.标准数据集上的实验结果验证了所提方法的有效性.

Dynamically Determining Neighborhood Parameter for Locally Linear Embedding

Locally linear embedding is a kind of very competitive nonlinear dimensionality reduction with good representational capacity for a broader range of manifolds and high computational efficiency.However,they are based on the assumption that the whole data manifolds are evenly distributed so that they determine the neighborhood for all points with the same neighborhood size.Accordingly,they fail to nicely deal with most real problems that are unevenly distributed.This paper presents a new approach that takes the general conceptual framework of Hessian locally linear embedding so as to guarantee its correctness in the setting of local isometry to an open connected subset but dynamically determines the local neighborhood size for each point.This approach estimates the approximate geodesic distance between any two points by the shortest path in the local neighborhood graph,and then determines the neighborhood size for each point by using the relationship between its local estimated geodesic distance matrix and local Euclidean distance matrix.This approach has clear geometry intuition as well as the better performance and stability to deal with the sparsely sampled or noise contaminated data sets that are often unevenly distributed.The conducted experiments on benchmark data sets validate the proposed approach.