Relative Transformation with CamNN Applied to Isometric Embedding

Neighborhood selection is one of the most important link in low-dimensional representations of high-dimensional data sets. Also, a good distance measure among the data points is where the shoe pinches. In this paper, we use the cam weighted distance to find a more flexible neighborhood of a data point in a newly-created space of r-isomap algorithm. It is a major advantage of r-isomap to optimize the process of intrinsic structure of the local information in a data set. Short-circuit edges are reduced in a certain extent because of the relative transformation space which is constructed in r-isomap. Furthermore, we can get a well performance on both orientation and scale adaptive side, because we utilize the cam weighted distance to search the neighborhood of a data point. It has been proved that this distance measure is more efficient than the Euclidean distance. Experiments demonstrated that the proposed method can give better results on dimension reduction than r-isomap, Weighted Locally Linear Embedding (WLLE) and some other approaches on the data sets which have obvious classifications. Especially robust to data sets with noise.