基于Kernel Rank-order距离的重构权重局部线性嵌入算法

RECONSTRUCTION WEIGHT LOCAL LINEAR EMBEDDING ALGORITHM BASED ON KERNEL RANK-ORDER DISTANCE

针对局部线性嵌入算法(Local Linear Embedding,LLE)短路、离群点影响大和结构信息缺乏等问题,提出基于Kernel Rank-order距离的重构权重局部线性嵌入算法(Reconstruction weight Local Linear Embedding algorithm based on Kernel Rank-order distance,KRLLE)。用核函数将样本点映射到高维使其更加线性可分,进而获得较好的近邻点集;计算重构权重系数进而得到加权重构权重,重构权重系数根据两点间相关性越大对重构贡献越大的特性来减小离群点的影响,并利用两点间的欧氏距离与测地线距离之比有效地将短路点排除在外;根据加权重构权重得到低维嵌入坐标。在ORL、Yale人脸库和MNIST手写体数据库上的实验表明,KRLLE对离群点具有更好的鲁棒性并且由于增加了结构信息,识别率得到了提高。

Local linear embedding(LLE)has problems such as short circuit,large outlier influence and lack of structural information.In order to solve the above problem,we propose the Reconstruction weight local linear embedding algorithm based on Kernel Rank-order distance(KRLLE).KRLLE firstly used the kernel function to map the sample points to a higher dimension to make them more linearly separable,and then obtained a better set of neighbor points.Secondly,the reconstruction weight coefficient was calculated to obtain the weighted reconstruction weight.The reconstruction weight coefficient was used to reduce the influence of outliers according to the characteristic that the greater the correlation between the two points,the greater the contribution to the reconstruction.The ratio of Euclidean distance to the geodesic distance between two points was used to effectively exclude the short-circuit points.Finally,the low dimensional embedded coordinates were obtained according to the weighted reconstruction weight.Experiments on the ORL,Yale face database and MNIST handwritten database show that KRLLE has better robustness for outliers.And the increase of structural information recognition rate has been improved.