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.