Extended ISOMAP based on neighborhood sets relation

The isometric feature mapping (Isomap) method has demonstrated promising results in finding low-dimensional manifolds from data points in high-dimensional input space. Isomap has one free parameter (number of nearest neighbours K or neighbourhood radius ε), which has to be specified manually. This paper presents a novel method called Hierarchical Neighbourhood Technique (HNT), in order to obtain a 'safe' neighborhood for resolving the "abnormal" phenomenon including short-circuit and sensitiveness to critical outliers widely existing in Isomap. The robust and small neighborhood of a sample point is obtained based on the correlation between two neighbors' neighborhood sets, and then continuously enlarge the range of stable neighborhood through the ordered accumulation of robust and relatively small region, then, a local Gaussian model is used for enhancing the ability of discrimination in image visualization. Experiments with symmetrical data, as well as real-world images, demonstrate that conventional methods combined with HNT can learn robust intrinsic geometric structures of the data, yield stable embeddings and have an excellent performance in discriminative image visualization.