摘要：The construction of similarity relationship amongdata points plays a critical role in manifold learning.There exist two popular schemes, i.e., pairwise-distancebased similarity and reconstruction coefficient based similarity.Existing works only have involved one scheme of them.These two schemes have different drawbacks. For pairwisedistancebased similarity graph algorithms, they are sensitiveto the noise and outliers. For reconstruction coefficient basedsimilarity graph algorithms, they need sufficient sampleddata and the neighborhood size is sensitive. This paperproposes a novel algorithm, called Local NeighborhoodEmbedding (LNE), which preserves pairwise-distance basedsimilarity and reconstruction coefficient based similarity forfinding the latent low dimensional structure of data. It hasfollowing three advantages: Firstly, it is insensitive to thechoice of neighborhood size; Secondly, it is robust to thenoise; Thirdly, It works well even in under-sampled case.Furthermore, the proposed objective function has a closedformsolution, which means it has a low computationalcomplexity, and the experimental results illustrate that LNEhas a competitive performance in dimensionality reduction.
